START HERE

About Basecalc

Basecalc is my ongoing research lab for harmonic patterns - a place where numbers, geometry, music, architecture, and astronomy are explored as one interconnected language. Instead of asking you to believe anything, it gives you tools: calculators, tables, visualizations, and reference data so you can verify and experiment for yourself.

Quick note: this page asks more than a 10-second scroll. Knowledge is not free - it needs attention to pay. Pay with focus and it pays back in deeper understanding of geometry, architecture, music harmony, astronomic cycles, and scripture.

For architects, designers, musicians, and anyone who wants to learn (or unlearn) beyond school: this page is a hands-on lab. Use it to test the golden section on real sizes, tune by ear with 432/440 Hz tables, explore the circle of fifths, and spot repeating number families that map across space, sound, and time. It is not theory for theory's sake; it is a practical way to improve proportions, voicings, and layouts while building a clearer sense of pattern in the world.

The goal of Basecalc is not to sell a doctrine, but to offer a playground for curiosity: a space where a musical note, a pyramid dimension, a planetary cycle, and a simple fraction can all be seen as different expressions of underlying harmonic relationships. If you are a designer, musician, architect, scientist, or just a fascinated nerd with a calculator, Basecalc invites you to dive in, test the patterns, and draw your own conclusions.

432 Hertz & Root 9 - A Simple Introduction

This page is a playground for the numbers behind music, myth, sacred geometry and time cycles. You can follow how the same few harmonics repeat from tuning (432 Hz) to Platonic solids and the 25,920 year "Great Year".

EXPLORE KEY NUMBERS JUMP TO HARMONIC BASE CALCULATOR TOOL JUMP TO PERSONAL PROPORTIONS TOOL

Why do numbers like 3, 6, 9, 72, 216, 432, 864 and 25920 appear in music, myth, geometry, astronomy and ancient architecture? This page lets you explore that question directly by showing how the same numbers repeat in different counting systems and scales.

432 Hz is sometimes described as a "natural" or "cosmic" tuning, not because physics has confirmed a single frequency for the universe, but because 432 fits a 3 based harmonic ladder (root 9) that reappears in Maya calendars, Hindu Yuga cycles, pyramid proportions, biblical number sets and the 25920 year precession cycle. The claim is symbolic, not scientific, but the number patterns themselves are real, measurable and testable on this page.

Example: The equinox point shifts approx. 1 degree every about 72 years. Multiply 72 by 360 degrees and you get about 25920 years, the so called Great Year. Notice how 72 -> 216 -> 432 -> 864 -> 25920 is the same harmonic sequence scaled up.

These same number paths also appear in geometry. The basic polygons of "sacred" or classical geometry follow the same 3 based logic: the circle (infinite sides), the triangle (3), the square (4), the pentagon / pentagram (5 and the golden ratio), and the hexagon (6) which tiles perfectly inside a circle of 360 degrees. From these come the five Platonic solids, each built from one repeating polygon, and all fitting inside the sphere by harmonic angles of 72, 90, 108 and 120 degrees. The page tools let you trace how these shapes, angles and number bases line up with the same 3-6-9 ladder used in the 432 family.

Harmonic Spiral Geometry - Nested Mandalas

Harmonic spirals nested in circular symmetry: left pattern reveals 6 fold coherence, right pattern multiplies through recursive 12 fold geometry.

Click the image to view it larger.

Base 10 and Base 60

Different civilizations counted in different bases. Understanding that makes the repeating patterns easier to see:

Base Used For Meaning on this page
Base 10 trade, measuring objects, money, engineering Form (matter, things you can weigh or build)
Base 60 time (60 s, 60 min), 360 degree circles, astronomy Flow (cycles, motion, sky geometry)

The tools on this page let you switch between bases and see how the same number behaves differently depending on how you count. When 6 (flow) and 10 (form) meet, you get 60: the bridge between matter and motion.

What You Can Do Here

No belief required: just test the numbers and decide for yourself whether the pattern is coincidence, design, or something in between.

12-Tone Harmony & the Circle of Fifths
Grand piano

Short Intro

Western keyboards and guitars use 12 equal steps per octave (equal temperament). Each step (a semitone) multiplies pitch by the same factor: 2^(1/12). If A4 = 440 Hz is your reference, any note n semitones away has f = 440 * 2^(n/12).

  • An octave is 12 semitones, so frequency doubles: ratio ~ 2:1.
  • A perfect fifth is 7 semitones up. In pure tuning it is ~ 3:2; in equal temperament it is 2^(7/12) (~1.498), very close to 3:2.
  • The circle of fifths walks by fifths (add +7 semitones each step). Because 7 and 12 share no common factor, this visits all 12 pitch classes (mod 12) before repeating.

Example (clockwise by fifths, wrapping by octaves): A → E → B → F# → C# → G# → D# → A# → F → C → G → D → A. Musically, close keys sit next to each other on this circle and share many notes, which is why the circle helps with chord progressions and key changes.

Why 432 Hz (instead of 440 Hz)

In equal temperament, every note is built from a reference pitch A4. Most modern music uses A4 = 440 Hz. Tuning to A4 = 432 Hz lowers every note by a small, fixed amount: ratio = 432/440 = 0.981818..., which is about -31.8 cents (roughly one third of a semitone).

Formulas

For any note n semitones away from A4:
  f_440(n) = 440 * 2^(n/12)
  f_432(n) = 432 * 2^(n/12) = f_440(n) * (432/440)

What listeners often report

  • 432 Hz can feel slightly warmer or less tense than 440 Hz (lower pitch by ~31.8 cents).
  • Some instruments and voices sit more comfortably; others sound nearly the same.
  • The difference is subtle on small speakers and stronger with acoustic material or wide dynamic mixes.

Numbers and harmony context

  • 432 = 2^4 * 3^3 (rich in 3-6-9 factors and sexagesimal links used in time and angle divisions).
  • Octaves still double (2:1), fifths remain 7 semitones; only the reference A4 changes.
  • Equal temperament stays the same; we simply shift the entire grid down by a constant ratio.
Reference A4 Shift vs 440 Perceived effect
440 Hz tuning 440.000 Hz 0 cents Modern standard; bright, consistent across gear.
432 Hz tuning 432.000 Hz -31.8 cents Slightly lower and often perceived as warmer or more relaxed.

Want to hear it yourself? We have examples rendered in 432 Hz in the Gallery section below on this page.

Tip: to retune a track, multiply every frequency by 432/440, or set your synth/DAW global reference to A4 = 432 Hz.

In equal temperament, each semitone multiplies frequency by 2^(1/12). If A4 is your reference (commonly 440 Hz), the frequency of any note n semitones away is f = A4 x 2^(n/12). An octave (12 semitones) doubles the frequency (ratio 2:1). The perfect fifth is close to a 3:2 ratio; stepping by fifths cycles through all 12 pitch classes (modulo the octave).

Circle of Fifths (equal temperament model)

Below is the cycle as simple note-to-note arrows. It adds 7 semitones mod 12 each step.

Other transpositions (same cycle pattern)

Just Intonation Intervals at A4 = 432 Hz

Frequencies are computed with: f_interval = 432 * ratio. These are pure (just) ratios. In 12-TET the actual frequencies differ slightly so you can play in all keys.

Interval Ratio Frequency (Hz)
Unison 1:1 432.00
Octave 2:1 864.00
Perfect Fifth 3:2 648.00
Perfect Fourth 4:3 576.00
Major Third 5:4 540.00
Minor Third 6:5 518.40
Major Sixth 5:3 720.00
Minor Sixth 8:5 691.20
Major Second 9:8 486.00
Minor Second 16:15 460.80
Major Seventh 15:8 810.00
Minor Seventh 9:5 777.60
Minor Seventh (alt.) 16:9 768.00

Note: Values are rounded to 2 decimal places for readability.

Piano notes cymatics pattern
Music notes vibration, made visible
Background: Maya, Yuga Cycles, Pyramid & Number Wisdom

Maya Long Count & 360-day View

El Castillo (Temple of Kukulcan) at Chichen Itza El Castillo (Temple of Kukulcan), Chichen Itza
Palenque in Mexico Palenque in Mexico (9 base-layers x 5 doors/windows x 4 sides x 2 top layers = 360; 360x3 = 1080, 360x4 = 1440)
  • Maya Long Count Calendar: 5,125.36 years × 5 = 25,626.8 ≈ precession of the equinoxes (4 sides × 9 steps × 3 parts per side × 4 = 432; doubling to 864 when you include the two top layers).
Maya Long Count Harmonic Table

Base-20 (vigesimal) system: The Maya used a base-20 count, reflecting the natural count of fingers and toes — a "hands and feet" mathematics. The third level (Tun) is adjusted to 18 × 20 = 360 to align with the solar year, showing harmony between celestial cycles and human measure.

Cycle hierarchy:
1 Kin = 1 day
1 Uinal = 20 Kin = 20 days
1 Tun = 18 Uinal = 360 days
1 Katun = 20 Tun = 7,200 days ≈ 19.7 years
1 Baktun = 20 Katun = 144,000 days ≈ 394.26 years
13 Baktun = 1 Great Cycle = 1,872,000 days ≈ 5,125.36 years

Precessional harmony: Five Maya Great Cycles ≈ 25,626.8 years, nearly equal to Earth’s precessional year (~25,920 years). This resonance unites Maya, Hindu, and Sumerian cosmologies through shared numeric constants: 3,000, 6,000, 9,000, 12,000, 24,000, 36,000, 54,000, 72,000, 108,000, 144,000, 432,000, 72, 216, 8,640, 43,200. Each expresses a fractal scaling of time and consciousness.

Numerical synthesis:
– 360 days (Tun) ↔ 360-degree circle ↔ solar year
– 144,000 days (Baktun) ↔ Revelation / pyramid ratio key
– 72 years per degree ↔ precession constant
– 432 Hz ↔ "cosmic" base tone in tuning lore
– 864,000 miles (sun diameter) ↔ mirrored in Maya and Hindu scales

Fractal time concept: The Maya viewed time as recursive — each unit a seed of the next. Kin : Uinal : Tun : Katun : Baktun form a living sequence of micro-to-macro harmony, echoing the same base-6, 12, 60 resonances found in other sacred systems.

Maya Unit Count (days) Equivalent years Harmonic relation
Kin11 dayUnit of life / heartbeat
Uinal200.0548 yr20 digits — base of creation
Tun3600.986 yrCircle of degrees / solar year
Katun7,20019.7 yr≈ lunar node cycles
Baktun144,000394.26 yr144 = 12² — completion code
13 Baktun1,872,0005,125.36 yr1 Great Cycle / Mayan Age
5 × 13 Baktun9,360,00025,626.8 yr≈ precession of the equinoxes
Ancient 360-day year view

Many ancient systems modeled the year as 360 days. Interpreting the Maya Long Count through that lens makes several harmonics exact and easier to see.

Maya Unit Count (days) Years @ 365.2425 Years @ 360 Harmonic notes
Kin10.002740.00278Seed unit
Uinal200.05480.0556Base-20 digit cycle
Tun3600.9861.000Exactly 1 "ancient" year
Katun7,20019.7320.0020 "ancient" years
Baktun144,000394.26400.0020 Katun = 400 "ancient" years
13 Baktun1,872,0005,125.365,200.001 Great Cycle = 13 × 400 years
5 × 13 Baktun9,360,00025,626.826,000.0≈ precession (ancient rounding)

Takeaway: With a 360-day year, Tun = 1 year, Katun = 20 years, Baktun = 400 years, Great Cycle = 5,200 years, and Five Great Cycles = 26,000 years — making the precessional harmony very clean in an "ancient time" framework.

Hindu Yuga Cycles & Brahma Purana

Hindu Yugas

  • Kali Yuga = 432,000 years
  • Dvapara Yuga = 864,000 years
  • Treta Yuga = 1,296,000 years
  • Satya Yuga = 1,728,000 years
  • Total Maha Yuga = 4,320,000 years
Vedic Time Cycles (Maha Yuga = 4,320,000 human years)
Yuga / Phase Divine
years		 Human
years		 Human / 360 = divine Total divine
(cycle)		 Total human
(cycle)
KALI YUGA
Sandhya10036,000100
Kali1,000360,0001,0001,200432,000
Sandhyamsa10036,000100
DVAPARA YUGA
Sandhya20072,000200
Dvapara2,000720,0002,0002,400864,000
Sandhyamsa20072,000200
TRETA YUGA
Sandhya300108,000300
Treta3,0001,080,0003,0003,6001,296,000
Sandhyamsa300108,000300
SATYA YUGA
Sandhya400144,000400
Satya4,0001,440,0004,0004,8001,728,000
Sandhyamsa400144,000400
TOTAL MAHAYUGA
TOTAL 12,000 4,320,000 12,000 12,000 4,320,000
In Vedic cosmology, 1 divine year equals 360 human years. Notice how the digital roots collapse to 9.
Kailasa Temple, Ellora (Cave 16) Kailasa Temple, Ellora — a monolithic "yuga-scale" symbol in stone.
Brahma Purana — overview, structure, and number patterns

The Brahma Purana is one of the 18 Maha Puranas. Despite the title it is not only about Brahma. It mixes sacred geography, cosmology, legends, genealogies, temple lore, and pilgrimage guides. Many chapters praise Surya (the sun) and major tirtha regions, especially the Godavari basin and coastal Odisha (for example Jagannath-Puri traditions and a sun-temple focus). The text exists in layered recensions compiled over many centuries.

  • Traditional classification: one of the Rajasika group in some lists.
  • Nickname found in some traditions: Saura Purana (sun-focused sections).
  • Large share of chapters are tirtha-mahatmya (pilgrimage site glorifications).
  • Cosmology includes the seven-island world (sapta-dvipa), Mount Meru at the center, and yuga cycles.
  • Multiple redactions; content overlaps with other Puranas and epic material.
What it covers and how to map it into Basecalc
Topic What the text emphasizes Number pattern notes
Sapta-dvipa world Seven island-continents, each encircled by an ocean, concentric rings around Meru. 7 islands + 7 oceans gives a 7-layer alternation. Map to 7-scale degrees or 7x ring UI. DR(7)=7; base-7 motif sits well with base-60 ring ticks.
Mount Meru hub Meru stands at the cosmic center; four quarters marked by cardinal mountains and rivers flowing to the four directions. Fourfold symmetry for compass mapping. 4-way cross overlay and perfect-fourths metaphor in music view.
Surya focus Hymns and narratives around the sun, allied deities, and sun temples. Great for 12-month and 6-season wheels. Base-6 and base-12 toggles align with solar cycles and 12-TET metaphors.
Tirtha-mahatmya blocks Pilgrimage guides and holy place lore, esp. Godavari region and Odisha coastline. Cubit-inch-foot toggles and DR badges. Wayfinding numbers often compress to simple roots.
Genealogies and myths Lineages of kings and sages, creation cycles, avatars, and temple-origin legends. Layered timelines with base-6 grouping (6, 12, 24, 60).
Time cycles (yugas) Four ages in 4:3:2:1 proportion, summing to a maha-yuga. Direct 432 linkage: Kali 432,000 years; maha-yuga 4,320,000 years. Align to A=432 panel and DR checks.
Yuga cycle numbers (standard Purana scheme)
Yuga Proportion (relative) Years in a yuga Digital root of years Basecalc note
Satya (Krita) 4 1,728,000 DR(1728000)=1+7+2+8=18 -> 9 Factor-rich; 1728 = 12^3 echo
Treta 3 1,296,000 DR(1296000)=1+2+9+6=18 -> 9 1296 = 6^4 and 36^2
Dvapara 2 864,000 DR(864000)=8+6+4=18 -> 9 864 = 2 x 432
Kali 1 432,000 DR(432000)=4+3+2=9 Your A=432 bridge
Maha-yuga total 4+3+2+1 = 10 parts 4,320,000 DR(4320000)=9 432 x 10,000
Hindu and Buddhist Sites with 432-family Counts

Yuga numbers appear in architecture by simple counts and proportional encodings. Below are well-known cases where 432 and its near relatives (216, 108, 72) are visible in the design or element counts. This closes the Yuga background with concrete site examples.

Direct 432 count
  • Borobudur (Buddhist, Java, Indonesia, 8th-9th c.) - 432 seated Buddhas on the five square galleries. The three circular terraces carry 72 perforated stupas with Buddhas inside. Total is 504, but the 432 block is explicit and the 72 upper layer aligns with the same family.
Yuga magnitudes in plan measures
  • Angkor Wat (Hindu, Cambodia, early 12th c.) - Readings of the plan relate causeway and enclosure measures to Yuga numbers, including 432,000 and other canonical magnitudes (648,000, 864,000, 1,296,000). The temple is devoted to Vishnu and integrates cosmology into its layout.
Half and quarter harmonics of 432
  • Bayon (Buddhist, Angkor Thom, late 12th-13th c.) - Common description: 54 towers with 4 faces each, for a total near 216 faces. This is one half of 432. Counts vary with ruin state, but 54 x 4 is a standard summary.
  • Boudhanath Stupa (Buddhist, Kathmandu, largely 14th-15th c.) - Approximately 108 prayer wheels around the base, a quarter of 432. The 108 count is a standard sacred number in Buddhist practice.
Summary - Borobudur shows 432 directly in statue counts (plus 72 above). Angkor Wat encodes Yuga magnitudes such as 432,000 in its plan. Bayon clusters near 216 (half of 432). Boudhanath uses 108 (quarter of 432). These counts and measures tie the monuments to the same harmonic family used in the Yuga cycles.

Ancient Egypt / Great Pyramid

  • Base perimeter ≈ 3,024 ft = 4 × 756 ft; height built around ~51.84 degrees and harmonic ratios.
Golden-ratio pyramid diagram
Golden-ratio pyramid diagram
Great Pyramid section (cubits)
Great Pyramid section (cubits)
Giza Pyramids - cubits, feet/inches, meters, digital roots, root-9, and 12-TET (A4 = 432 and 440)
Pyramid Base:height ratio Base (RC) Height (RC) Base (Heb cubits) Height (Heb cubits) Base (ft in) Height (ft in) Base (m) Height (m) DR(Base RC) DR(Height RC) DR pair (B+H) DR(ratio digits) Root-9? Nearest 12-TET note Cents offset Freq A4=432 (Hz) Freq A4=440 (Hz)
Khufu (G1) 11:7 440.0 RC 280.0 RC 503.9 HC 320.7 HC 755 ft 10.2 in 480 ft 12.0 in 230.38 m 146.61 m 8 1 9 9 YES F -17.5 c 678.9 691.4
Khafre (G2) 3:2 411.0 RC 274.0 RC 470.7 HC 313.8 HC 706 ft 0.4 in 470 ft 8.3 in 215.20 m 143.47 m 6 4 1 5 NO E +2.0 c 648.0 660.0
Menkaure (G3) 8:5 200.0 RC 125.0 RC 229.0 HC 143.2 HC 343 ft 6.8 in 214 ft 8.8 in 104.72 m 65.45 m 2 8 1 4 NO F +13.7 c 691.2 704.0
G1-a (Hetepheres I) 18:11 94.5 RC 57.8 RC 108.3 HC 66.2 HC 162 ft 4.8 in 99 ft 2.9 in 49.50 m 30.25 m 5 4 9 2 YES F# -47.4 c 706.9 720.0
G1-b (Meritites I) 5:3 95.5 RC 57.3 RC 109.4 HC 65.6 HC 164 ft 0.5 in 98 ft 5.1 in 50.00 m 30.00 m 5 3 8 8 NO F# -15.6 c 720.0 733.3
G1-c (Henutsen) 25:16 88.3 RC 56.5 RC 101.2 HC 64.7 HC 151 ft 8.9 in 97 ft 1.4 in 46.25 m 29.60 m 7 3 1 5 NO F -27.4 c 675.0 687.5

RC = Egyptian royal cubit (~0.5236 m, ~20.62 in). Hebrew cubit = 18.00 in (~0.4572 m). DR(x) = digital root of an integer x reduced to one digit by repeated digit sums. DR pair is DR(Base RC) + DR(Height RC) reduced to one digit. DR(ratio digits) is the digital root of the sum of all digits in the ratio (for example 11:7 gives 1+1+7 = 9). Root-9 is YES if DR pair equals 9 or DR(ratio digits) equals 9. 12-TET mapping: treat the base:height ratio as a frequency multiple above A; nearest note, cents offset and the frequencies at A4 = 432 Hz and A4 = 440 Hz are shown (Freq = A4 * ratio).

Hebrew Cubit (Common / Short) & Earth Ratios

HEBREW CUBIT (COMMON / SHORT)  ~ 0.4572 m  =  18 in

440 HC -> 201.168 m -> 660.000 ft (exact 660 ft 0 in) -> 7920.0 in
  base-6: 100400, base-60: 2:12, root 9: 7+9+2+0 = 18 -> 1+8 = 9

280 HC -> 128.016 m -> 420.000 ft (exact 420 ft 0 in) -> 5040.0 in
  base-6: 35200, base-60: 1:24, root 9: 5+0+4+0 = 9

NOTE:
  The meter is defined by fixing the speed of light c = 299 792 458 m/s
  and defining the second via the cesium-133 hyperfine transition
  frequency ("atomic vibration") of 9 192 631 770 Hz.
  So the meter is tied to light speed and that atomic frequency,
  not to human anatomy.
  • Great Pyramid of Giza & Earth ratios: The pyramid's height and base perimeter have been claimed to scale to the Earth at a ratio of ~1 : 43,200 — meaning that if the pyramid's dimensions are multiplied by 43,200, they approximate Earth's radius or circumference.
  • Because a day has 86,400 seconds, 1/43,200 of a day is exactly 2 seconds, which is why people say "every 2 seconds" of Earth's rotation echoes that same ratio.
  • The number 43,200 factors into 72 × 600 and is linked to both precession cycles (72 years per degree) and time measurement (43,200 = 60 × 60 × 12).
  • The 36 decans were star groups used by the ancient Egyptians to divide the night sky and the year into equal parts. Each decan rose on the horizon every 10 days, marking a "week" in their 360-day year (36 × 10 = 360 days, plus 5 festival days). At night, each decan's rising signaled a new hour, so priests could tell time by the stars. Later, the Greeks adopted the 36 decans into astrology, making them 10-degree divisions of each zodiac sign, each with its own deity or planetary ruler. In short: Egyptian decans = 36 star clocks for time + 36 calendar weeks, later forming the backbone of zodiac astrology.
  • Note: These numerical claims are debated within mainstream scholarship; they are often treated as symbolic or esoteric correspondences rather than hard archaeological proof.

Pre-diluvian "God Kings" of Sumeria

Pre-flood rulers and how long each one was said to reign. The total adds up to 432,000 years, which ties directly into the 432 / 3-6-9 harmonic timelines.

Name of king Years of reign Digital root of years
Aloros36,0009
Alaporos10,8009
Amelon46,8009
Ammenon43,2009
Megalaros64,8009
Daonos36,0009
Euedoroches64,8009
Amempsinos36,0009
Opartes28,8009
Xisuthros64,8009
TOTAL YEARS 432,000 9

Every reign length reduces to digital root 9. The grand total, 432,000 years, is one of the core "432" harmonic numbers used in cosmology lore, Vedic/Yuga cycle talk, and sacred time-base systems. It is the same 432 resonance already tracked in tuning, precession, and calendar systems on this page.

Harmonic Notes

  • 432 Hz: often framed as resonating with a "natural" harmonic scale.
  • Base 60 (Sumerian) used for time, angle and celestial calculations — harmonically linked to base 6 and base 10.
  • 72 years per degree of the Great Year (25,920 / 360 = 72).
  • 12 tribes of Israel — root of 144 (12 × 12 = 144), symbol of completeness and order. The number 12 recurs: 12 months, 12 zodiac signs, 12 hours of day and night, and 12 tones in the musical octave.
These systems are not isolated. They rhyme across cultures, timelines and languages through shared number patterns — especially 3, 6, 9, 72, 432 and their scaled relatives.

Qur'an Numbers (explicit items & composition facts)

This section focuses on numbers that are either explicitly stated in the Qur'an text itself (for example 19, 12, 4, 7) or are standard composition facts (114 surahs, 6,236 verses in the Hafs/Kufa tradition), then maps them into base-6, base-60 and digital-root views.

  • Qur'an (Kufa tradition) — the Qur'an contains 6,236 verses (Hafs/Kufa recension). Symbolically, 6x2x3x6 = 216 → digital root 9, echoing the same 9-based harmonic cycle that shows up in other sacred systems.
    • Item Source Decimal Base-6 Base-60 Digital root Basecalc note
    "Over it are nineteen" Q 74:30 19 31 0:19 DR(19)=1 Prime; seed for 19-themed studies
    Months in a year Q 9:36 12 20 0:12 DR(12)=3 Maps to base-6 and base-12 cycles
    Sacred months (subset of 12) Q 9:36 4 4 0:04 DR(4)=4 Quartering marker; 4 seasons metaphor
    Seven heavens Q 41:12; 67:3 7 11 0:07 DR(7)=7 Natural fit for 7-ring or 7-degree UI
    Surah count (canonical) Composition fact 114 310 1:54 DR(114)=6 114 = 19 x 6 (ties 19 to base-6)
    Verse count (Hafs/Kufa tradition) Composition fact 6,236 43444 103:56 6+2+3+6 = 17 -> DR(6236)=8 Symbolically, 6x2x3x6 = 216 -> DR(216)=9
    Basmala distribution Composition fact 114 total 310 1:54 DR(114)=6 Sura 9 lacks it; Sura 27 has it twice
    About "Code 19": Q 74:30 explicitly mentions nineteen. Some writers extend this into large numeric schemes (letter counts, initials, basmala placements). These depend on which script and counting tradition you choose, so results vary and are debated. Basecalc sticks to explicit, checkable counts (like 19, 12 months, 7 heavens, 114 surahs, and standard verse totals), which map cleanly to base-6/base-60 and digital-root analysis.

    Mesopotamian Clay Tablets: Base-60 & Cosmic Numbers

    • Mathematics (base 60): place-value arithmetic, reciprocals, tables, geometry aids. Connected with 60 minutes, 60 seconds, 360 degrees.
    • Astronomy/astrology: series MUL.APIN with a schematic 12 x 30 = 360-day year, star risings/settings, and the ecliptic band used for zodiacal schemes.
    • Right-triangle lists: tablet Plimpton 322 with Pythagorean-type triples in sexagesimal, likely for surveying/geometry.
    • Eclipse records: Late Babylonian diaries and the Saros cycle (~18 years) for eclipse prediction.
    • King lists and long chronologies: Sumerian King List uses units based on 60 (soss=60, ner=600, sar=3600); later Babylonian writer Berossus totals antediluvian reigns to 432,000 years.
    Numbers explicitly attested and how they align with pattern study
    Number motif Attested where Meaning in context Notes for base-6/10/12/60 and DR
    60 (base) and 360 Babylonian mathematics traditions Sexagesimal place value; time/angle divisions (60x60, 360 degrees) Direct mapping to base-60; 360 fits circle/degree structures; DR(360)=9
    12, 30, 360 (schematic year) MUL.APIN tablets 12 months x 30 days for calendrical schemes and star lists Aligns with base-12 and base-60; DR(360)=9; useful for month/season wheels
    Right-triangle ratios (triples) Plimpton 322 (Old Babylonian) Lists integer triples in sexagesimal; geometric surveying tool Ratios can be shown in base-60 and compared with musical intervals
    ~18-year eclipse cycle Late Babylonian astronomy (Saros) 223 synodic months ~ 18 years 11 days used for eclipse prediction Connects with 18 and 36 in DR ladders; works cleanly in base-6/60 clocks
    Units of 60/600/3600 in reigns Sumerian King List (various copies) Reigns expressed in soss, ner, sar (60-based units) Pure base-60 stacking without extra assumptions; DR often reduces to 3 or 9
    432,000 (antediluvian total) Berossus (Hellenistic-era Babyloniaca) Ten kings before the flood totaling 432,000 years (literary number) Links to 432-pattern studies seen across traditions; DR(432000)=9
    Notes: 1) Base 60, 12-month schemata, and 360-degree frameworks are standard features of Mesopotamian sources. 2) Plimpton 322 demonstrates sophisticated ratio work in sexagesimal. 3) Eclipse Saros is a practical ~18-year cycle in Late Babylonian records. 4) The 432,000 total appears in Berossus (later tradition) and is labeled as a literary value.
    Greek-Roman Temples of Paestum
    Paestum temples view 1
    Paestum, Campania, southern Italy (inside the Paestum archaeological park).
    Paestum temples view 2
    Three very well-preserved Doric temples stand here within the ancient city grid.
    Who, when, where
    • Where: Paestum (ancient Poseidonia), Campania, southern Italy, near the Tyrrhenian coast.
    • Temple of Hera I (the "Basilica"): Archaic Doric, about 560-550 BC. Greek dedication to Hera.
    • Temple of Hera II (often called "Temple of Neptune"): Early Classical Doric, about 460-450 BC. Now commonly identified as a second Hera temple.
    • Temple of Athena (earlier called "Ceres"): Late Archaic, about 510-500 BC. Doric outside, Ionic elements inside; dedication inferred from finds of the goddess.
    Column counts and simple math

    Read what is in plain sight by counting columns without double-counting the corner columns.

    • Example A: 6x2 + 12x2 = 36 outer columns (6x12 = 72 family).
    • Example B: 9x2 + 16x2 = 50 outer columns, and the product front 9 x side 16 = 144.
    • Both 72 and 144 reduce to digital root 9. These counts align with the 3-6-9 and 432-type harmonics lens.
    Steps and platform terms

    Most Greek temples stand on a 3-step base called the crepidoma (often just "crepis"). The top step is the stylobate, where the columns stand. The lower step(s) are the stereobate. At Paestum, the temples follow the usual 3-step scheme.

    • Crepidoma / crepis: the whole stepped platform (typically 3 steps).
    • Stylobate: the top step; column bases sit on this level.
    • Stereobate: the lower step or steps under the stylobate.
    Resonance note with the 3 steps
    • If the peristyle count gives 72 and there are 3 steps, 72 x 3 = 216.
    • If the peristyle count gives 144 and there are 3 steps, 144 x 3 = 432.
    • Both 216 and 432 reduce to digital root 9. "Root 9" read is visible in the common 3-step base used across Doric, Ionic, and Corinthian practice.

    Classical Planets and Gods

    Body / Aspect Egypt Greek Roman Mesopotamian (Babylon / Assyria) Maya / Aztec
    Sun Ra, Ra-Horakhty Helios, Apollo Sol, Sol Invictus Utu, Shamash Kinich Ajaw (Maya), Tonatiuh, Huitzilopochtli (Aztec)
    Moon Khonsu, Thoth Selene, Artemis Luna, Diana Nanna, Sin Ix Chel (Maya), Tecciztecatl, Coyolxauhqui (Aztec)
    Mercury Thoth Hermes Mercury Nabu (Nebo) No single clear Mercury god preserved
    Venus (Morning / Evening Star) Hathor, Isis Aphrodite Venus Inanna, Ishtar Chak Ek (Maya), Quetzalcoatl as Tlahuizcalpantecuhtli, Xolotl (Aztec)
    Mars Horus (Horus the Red, Horus of the Horizon) Ares Mars Nergal Linked to war gods, not one fixed name
    Jupiter Horus (Illumines the Two Lands), sometimes Amun-Jupiter Zeus Jupiter (Jove) Marduk Linked to high sky / creator gods, not one fixed name
    Saturn Horus (Bull of the Sky) Cronus (Kronos) Saturn Ninurta (Ninib) Tracked astronomically, no single named Saturn god
    Horizon / Dawn Ra-Horakhty, Aker Eos Aurora Sun rising through the eastern gate Chak Ek at dawn (Maya), Tlahuizcalpantecuhtli (Aztec)
    Sky / Heavens Nut Ouranos, Zeus Caelus, Jupiter Anu Itzamna (Maya), Citlalicue (Aztec)
    Bright star example Sopdet (Sirius) Various star heroes and constellations Bright stars as divine signs, Venus as brightest Ninsianna and other star forms Star creators like Citlalicue, Citlalatonac; Venus again key

    Major Festival Date Clusters for Sun and Planet Gods

    Dates are approximate modern (Gregorian) equivalents of ancient calendars.

    Cluster Culture God(s) Festival / Focus Approx. Date
    Winter solstice / new Sun Rome Saturn, Sol Saturnalia; Dies Natalis Solis Invicti approx. 17-23 Dec; 25 Dec
    Winter solstice / new Sun Aztec Huitzilopochtli (Sun and war) Panquetzaliztli (birth of the Sun) approx. late Nov to early Jan
    Summer New Year / Sirius Egypt Ra, Isis, Sopdet, Nut Wepet Renpet (Opening of the Year) approx. mid July to early Aug
    Summer New Year Athens (Greek) Zeus, Olympian gods Athenian civic New Year (Hekatombaion 1) first new moon after solstice (Jul or Aug)
    Spring equinox / New Year Babylon / Assyria Marduk, Nabu, Shamash, Sin, Ishtar Akitu New Year approx. March to April
    Spring war / renewal Rome Mars Equirria horse races; start of campaign season 27 Feb; 14 Mar
    Spring / first fruits Athens (Greek) Apollo, Artemis Thargelia (purification and first harvest) approx. late May
    🧩 Word / Gematria Match: Embedded Sacred Lexicon

    Key Number & Word Links

    • 1080 → "Holy Ghost" (Greek: Pneuma Hagion)
    • 432 → tuning frequency / "Heaven" harmonic / 12 × 36
    • 666 → "Calculation key", resonance distortion or mirror code
    • 144000 → Book of Revelation, harmonic completion
    • 888 → "Jesus" in Greek
    • 72 → Divine names in Kabbalah / 1° precession shift
    Torah Harmonic Correspondences
    • 3 → Avraham, Yitzhak, Yaakov — patriarchal triad, foundation of faith
    • 6 → Sheshet Yemei Bereshit — six days of Creation
    • 9 → Emet (אמת) = 441 → 4 + 4 + 1 = 9 — "Truth", seal of God
    • 12 → Shivtei Yisrael — twelve tribes of Israel
    • 24 → books of the Tanakh (תנך) — 24 canonical writings
    • 36 → Lamed-Vav Tzadikim — 36 hidden righteous souls
    • 54 → Sidrei Torah Parashot — 54 weekly Torah portions
    • 72 → Shem Ha-Meforash — 72-fold Divine Name (Exodus 14:19–21)
    • 108 → Elohim (אלהים) ≈ 108, symbolic completion of divine order
    • 216 → Gevurah (גבורה) = 216 — "strength", one of God's emanations
    • 360 → HaGalgal (הגלגל) — celestial wheel, completeness of cycle
    • 432 → David (דוד) = 14; 432 / 3 = 144 — royal lineage harmonic
    • 540 → Yisrael (ישראל) = 541 ≈ 540 — symbolic unity of the people
    • 720 → Keter + Malkhut — crown and kingdom, upper and lower union
    • 1080 → Ruach Ha-Kodesh — Holy Spirit (aligns with Greek "Holy Ghost")
    • 2160 → Light of the Moon — lunar sphere ≈ 2160 mile radius
    • 4320 → Yovel cycle — 120 × 36 = 4320, symbol of renewal and release
    • 8640 → Ohr Ha-Olam (אור העולם) — "Light of the world", doubled 4320

    Hebrew Gematria (Short Intro + Table)

    Gematria is a simple system where each Hebrew letter equals a number. Add the letter values of a word to get its total. In Torah study, this does not replace the plain meaning; it highlights patterns and supports ideas found in the text.

    Name Hebrew Value Name Hebrew Value Name Hebrew Value
    Alefא1 Yodי10 Qofק100
    Betב2 Kafכ20 Reshר200
    Gimelג3 Lamedל30 Shinש300
    Daletד4 Memמ40 Tavת400
    Heה5 Nunנ50    
    Vavו6 Samekhס60    
    Zayinז7 Ayinע70    
    Chetח8 Peפ80    
    Tetט9 Tsadiצ90    
    • Standard values run from 1 to 400 (Alef..Tav).
    • Mispar Katan: reduce a total by summing its digits to 1..9 (example: 611 => 6+1+1 = 8).
    • To compute a word: add each letter value. Example: Torah = Tav(400)+Vav(6)+Resh(200)+He(5) = 611.
    🔍 Visual Base Conversion (Base 10 → Chosen Base)

    Enter a base-10 number, pick a base and press Convert. The steps below show the repeated division and the final digit string in the chosen base.

    Counting in Different Bases (Base 10, Base 6, Base 60)

    A base is the number of unique digits you use before you roll over to a new place. Place values grow by powers of the base: ones (base^0), base (base^1), base^2, base^3, and so on. To see the conversion, fill in a number and press your button above.

    • Base 10 (0..9): what most of us use. After 9 comes 10 (one ten and zero ones).
    • Base 6 (0..5): after 5 comes 10_6 (one six and zero ones). Examples below.
    • Base 60 (0..59): after 59 comes 10_60 (one sixty and zero ones). Think clocks: 60 seconds = 1 minute.
    Idea Base 10 Base 6 Base 60
    Digits used 0..9 0..5 0..59
    First rollover 9 -> 10 5 -> 10_6 59 -> 10_60
    Place values 1, 10, 100, 1000, ... 1, 6, 36, 216, ... 1, 60, 3600, 216000, ...

    Tiny Counting Examples

    Base 10 (0..12):
0, 1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11, 12
        
    Base 6 (0..14_6):
0, 1, 2, 3, 4, 5,
10_6, 11_6, 12_6,
13_6, 14_6
        
    Base 60 (0..11_60):
0, 1, 2, ... 58, 59,
10_60, 11_60

    How to Convert (conceptual)

    • Place-value view: write the number as sums of powers of the base.
    • Division view: divide by the base, record the remainder, repeat with the quotient; read remainders backward.
    • Try it: enter a number and press your button above to see its form in base 6 or base 60.
    ♠ Binary Doubling Ladder × 3-6-9 Digital-Root Code

    This section shows the classic binary doubling chain 1 → 2 → 4 → 8 → 16 → 32 → ... and compares each value's digital root (sum of digits reduced to 1-9). The key observation: the digital roots of powers of two cycle as 2, 4, 8, 7, 5, 1 and never hit 3, 6, or 9. That is the "3-6-9 does not appear in binary roots" idea.

    Examples to Get the Digital Root

    • 18 → 1 + 8 = 9
    • 36 → 3 + 6 = 9
    • 32768 → 3 + 2 + 7 + 6 + 8 = 26 → 2 + 6 = 8

    Contrast: for powers of two, the digital-root cycle stays on the six-step wheel [2, 4, 8, 7, 5, 1]. No 3, 6, or 9 appear.

    PLATONIC
    Pentagram angles, Platonic solid geometry and zodiac precession woven into one "time geometry" lens: 72, 432, 2,160, 25,920 and their root-9 echoes.

    The pentagram inscribes a regular pentagon whose interior angle is 108°. Five such corners give 5 × 108° = 540° (digital root 5+4+0 = 9). These "holy" counts connect to zodiac/precession cycles long cited in esoteric math: 72, 432, 2,160, 25,920. We contrast the classical schema (25,920 years = 360° × 72 y/°) with a modern astronomical estimate (about 25,772 years).

    Platonic Set & Angle Links

    3x60° = 180° 60° 60° 60° 4x90° = 360° 90° 90° 90° 90° 5x108° = 540° 108°

    Key Numbers & Digital Roots

    🔶 Metatron’s Cube & Its 3D Parts
    Metatron Geometry

    Metatron’s Cube is the line network formed by connecting the centers of the 13 circles (Flower/Seed of Life extension). Within that network, the edge-graphs of all five Platonic solids can be embedded by appropriate selections of lines. This section maps those solids, their dualities, and their characteristic angle sums into the same 3‑6‑9 digital-root lens you’ve used elsewhere.

    All Five Platonic Solids — Angle & Digital-Root Map

    DR = 9 Contexts Across Platonic Solids

    Dualities & Star Forms

    Counts Inside the 13‑Circle Frame (conceptual)

    đź“ Biblical Numbers
    Biblical Numbers & Temple Geometry
    Cubits, 360-day Years & Root-9 Patterns
    Measurements in the Hebrew Bible / KJV form clean integer blocks. Here we track cubits, prophetic years and digital roots to see how many structures collapse back to 9.
    Gothic cathedral rose window and stained-glass panels
    Geometry in glass: rose window symmetry mirroring Biblical number structure.

    The Hebrew Bible / KJV gives physical and temporal measurements in clean integer blocks. We treat cubits as 18 inches = 1.5 feet, and regnal years as 360-day years the way ancient calendars are often modeled.

    Below: Solomon's Temple (1 Kings 6), the Ark of the Covenant (Exodus 25:10), and Jehoram timelines (2 Kings 3:1 KJV). For each value we also show the digital root: add the digits until you get one number.

    Solomon's Temple — Dimensions

    Zone Biblical Size (cubits) Size in Inches
    (1 cubit = 18")    		 Root of Inches
    (digit sum → 1 digit)    		 Same in Feet
    (12" = 1 ft)    		 Notes
    Main House
    ("the temple of the LORD")     		60 cubits long
    20 cubits wide
    30 cubits high
    1 Kings 6:2     		Length: 60×18" = 1080"
    Width: 20×18" = 360"
    Height: 30×18" = 540"
    Floor area: 1080" × 360" = 388,800 in²     		1080 → 1+0+8+0 = 9
    360 → 3+6+0 = 9
    540 → 5+4+0 = 9
    388,800 → 3+8+8+8+0+0 = 27 → 2+7 = 9     		Length: 90.0 ft
    Width: 30.0 ft
    Height: 45.0 ft
    Floor area: 2,700 ft²
    Volume: 121,500 ft³     		Long narrow hall lined with cedar and gold.
    Holy Place / Nave 40 cubits long
    20 cubits wide
    30 cubits high
    1 Kings 6:17-18     		Length: 40×18" = 720"
    Width: 20×18" = 360"
    Height: 30×18" = 540"     		720 → 7+2+0 = 9
    360 → 3+6+0 = 9
    540 → 5+4+0 = 9     		Length: 60.0 ft
    Width: 30.0 ft
    Height: 45.0 ft
    Floor area: 1,800 ft²
    Volume: 81,000 ft³     		Main working space for priestly ritual.
    Most Holy Place / Inner Sanctuary
    (Debir / "Holy of Holies")     		20 cubits × 20 cubits × 20 cubits
    1 Kings 6:20     		Edge: 20×18" = 360" per side
    (= 360" × 360" floor)     		360 → 3+6+0 = 9 Edge: 30.0 ft per side
    Floor area: 900 ft²
    Volume: 27,000 ft³     		Perfect cube, overlaid with gold. Restricted / presence zone.
    Porch / Vestibule (Entrance) 10 cubits deep
    20 cubits wide
    ~30 cubits high*
    1 Kings 6:3
    *Height ~30 cubits assumed to match the house in 6:2; 2 Chronicles 3:4 reads 120 cubits, often seen as a copy inflation.     		Depth: 10×18" = 180"
    Width: 20×18" = 360"
    Height: 30×18" = 540"     		180 → 1+8+0 = 9
    360 → 3+6+0 = 9
    540 → 5+4+0 = 9     		Depth: 15.0 ft
    Width: 30.0 ft
    Height: 45.0 ft
    Floor area: 450 ft²
    Volume: 20,250 ft³     		Entry hall / porch in front of the main door.

    Ratio / harmony note

    The core block of the Temple is 60 : 20 : 30 cubits (1 Kings 6:2 KJV). Reduce that and you are looking at clean integers (3 : 1 : 1.5 if you divide through by 20), then a 20-cubit cube for the Most Holy Place (1 Kings 6:20 KJV).

    Plain language: the Temple body is about 1080" long × 360" wide × 540" high (≈ 90 × 30 × 45 ft), and the inner gold room is a ~360" cube (≈ 30 ft cube). All inch values collapse to 9.

    Ark of the Covenant — Dimensions

    "And they shall make an ark of shittim wood: two cubits and a half shall be the length thereof, and a cubit and a half the breadth thereof, and a cubit and a half the height thereof." Exodus 25:10 KJV

    Conversion:
    1 cubit = 18 inches = 1.5 feet.

    Object Biblical Size (cubits) Size in Inches
    (1 cubit = 18")    		 Root of Inches
    (digit sum → 1 digit)    		 Same in Feet
    (12" = 1 ft)    		 Notes
    Ark of the Covenant
    Exodus 25:10 KJV     		Length: 2.5 cubits
    Width: 1.5 cubits
    Height: 1.5 cubits     		Length: 2.5×18" = 45"
    Width: 1.5×18" = 27"
    Height: 1.5×18" = 27"     		45 → 4+5 = 9
    27 → 2+7 = 9
    27 → 2+7 = 9     		Length: 45" ÷ 12 = 3.75 ft (≈ 3'9")
    Width: 27" ÷ 12 = 2.25 ft (≈ 2'3")
    Height: 27" ÷ 12 = 2.25 ft (≈ 2'3")
    Volume (outer box): ~18.98 ft³     		Gold-covered chest with rings and poles; carried by hand.

    Top surface / lid area:
    45" × 27" = 1,215 in².
    Root: 1+2+1+5 = 9.
    (Same in feet: 3.75 ft × 2.25 ft ≈ 8.44 ft²)

    Outer box volume (rectangular bound):
    45" × 27" × 27" = 32,805 in³.
    Root: 3+2+8+0+5 = 18 → 1+8 = 9.
    (≈ 18.98 ft³)

    Summary: about 45" × 27" × 27" (≈ 3.75 ft × 2.25 ft × 2.25 ft). Inch values resolve to 9.

    Noah's Ark ♦ Hebrew Cubit (18 in) shown in Inches and Feet, plus Base-6 and Base-60
    Bible ratio 300 x 50 x 30 cubits. Using the Hebrew/common cubit = 18.00 inches (1.5 ft). Digital roots are computed on base-10 values.
    Inches (5,400 x 900 x 540)
    Span Inches (base-10) Base-6 Base-60 (sexagesimal) Digital root (base-10)
    Length 5400 41000 1:30:0 9
    Width 900 4100 15:0 9
    Height 540 2300 9:0 9
    Feet (450 x 75 x 45)
    Span Feet (base-10) Base-6 Base-60 (sexagesimal) Digital root (base-10)
    Length 450 2030 7:30 9
    Width 75 203 1:15 3
    Height 45 113 45 9
    Cubit counts (300 x 50 x 30 cubits)
    Span Cubits (base-10) Base-6 Base-60 (sexagesimal) Digital root (base-10)
    Length 300 1220 5:0 3
    Width 50 122 50 5
    Height 30 50 30 3
    Notes: Base-6 uses digits 0-5. Base-60 values are colon-separated (most-significant to least), e.g., 1:30:0 means 1*60*60 + 30*60 + 0. Digital roots shown are computed on base-10 values. With 18-inch cubits, inch values 5400, 900, 540 are all multiples of 9, so they collapse to digital root 9.

    Total surface area = 2(LW + LH + WH) -> still DR 9 (sum of three 9s, then x2 keeps DR 9)
    Volume = 5,400 x 900 x 540 = 2,624,400,000 in^3 -> 2+6+2+4+4+0+0+0+0+0 = 18 -> 1+8 -> DR 9
    Total edge length = 4(L + W + H) = 4(5,400 + 900 + 540) = 27,360 in -> 2+7+3+6+0 = 18 -> 1+8 -> DR 9

    2 Kings 22 - Narrative Numbers mapped to the 432 Family

    This is a simple arithmetic lens: take the literal narrative numbers (age/year markers) and factor them into clean 432 multiples. No claim of author intent - just a pattern check you can verify.

    Text Narrative number Factor bridge 432 relation DR
    2 Kings 22:1 8 years old 8 x 54 = 432 432 = 8 x 54 8
    2 Kings 22:3 18th year 18 x 24 = 432 432 = 18 x 24 9
    Circle-time bridge 360 x 30 360 x 30 = 10,800 10,800 = 432 x 25 9
    Notes: DR = digital root (base-10 digit sum reduction). 432 -> 4+3+2 = 9. Also: 360 relates to 432 by 360 x (6/5) = 432.
    1 Esdras 5:15 - Literal 432 (Census List)
    Literal number: 432
    432 relation: 432 = 432 (direct occurrence)
    Digital root: 4+3+2 = 9
    Category: Direct literal 432
    2 Esdras 14:44-46 - The 24 Books (Public) -> 432 Bridge
    Literal number: 24 (books)
    Factor bridge: 24 x 18 = 432
    432 relation: 432 = 24 x 18
    Digital root: 4+3+2 = 9
    Category: Factor entry (24 is a clean 432 factor bridge)
    1 Esdras 5:9 - Literal 72 (inside a census number) -> 432 Bridge
    Literal number: Literal number: 72 (the "...seventy and two" tail)
    Factor bridge: 72 x 6 = 432
    432 relation: 432 = 72 x 6
    Digital root: 4+3+2 = 9
    Category: Factor entry (72 is a classic 432-family gateway)
    Tobit 14:2 - Literal 8 Years -> 432 Bridge
    Literal number: 8 (years)
    Factor bridge: 8 x 54 = 432
    432 relation: 432 = 8 x 54
    Digital root: 4+3+2 = 9
    Category: Factor entry (8 is a direct factor gateway to 432 via 54)
    Revelation 4:4 - 24 Elders / 24 Thrones -> 432 Bridge
    Literal number: 24 (elders / thrones)
    Factor bridge: 24 x 18 = 432
    432 relation: 432 = 24 x 18
    Digital root: 4+3+2 = 9
    Category: Factor entry (24)
    Luke 10:1 - 72 Sent Out -> 432 Bridge
    Literal number: 72 (seventy-two)
    Factor bridge: 72 x 6 = 432
    432 relation: 432 = 72 x 6
    Digital root: 4+3+2 = 9
    Category: Factor entry (72)
    Biblical Items * Hebrew cubit = 18 in * Inches, Feet, and Digital Roots
    Reference Cubits (L x W x H or dims) Inches (L x W x H) Feet (L x W x H) DR(inches)
    Table of Showbread (Ex 25:23) 2 x 1 x 1.5 36 x 18 x 27 3 x 1.5 x 2.25 9, 9, 9
    Altar of Incense (Ex 30:2) 1 x 1 x 2 18 x 18 x 36 1.5 x 1.5 x 3 9, 9, 9
    Altar of Burnt Offering (Ex 27:1) 5 x 5 x 3 90 x 90 x 54 7.5 x 7.5 x 4.5 9, 9, 9
    Tabernacle Court (Ex 27:18) L 100, W 50, H 5 1800, 900, 90 150, 75, 7.5 9, 9, 9
    Bronze Sea (1 Kgs 7:23) diam 10, circ 30, h 5 180, 540, 90 15, 45, 7.5 9, 9, 9
    Ezekiel's Reed (Ezek 40-43)
    Unit Definition Inches Feet DR(inches)
    1 Reed 6 cubits 108 9 9
    Remark: Using the Hebrew/common cubit at 18.00 inches (1.5 ft) causes many biblical dimensions to land on inch values that are multiples of 9. That is why the digital roots of the inch measures above often resolve to 9, and areas/volumes built from them tend to collapse back to 9 under digit-sum reduction.

    Jehoram (Joram) king of Israel — Time Math

    "Now Jehoram the son of Ahab began to reign over Israel in Samaria the eighteenth year of Jehoshaphat king of Judah, and reigned twelve years." 2 Kings 3:1 KJV

    We model an ancient / prophetic year as 360 days.

    Span Years Days @ 360-day year Root of Days
    (digit sum → 1 digit)
    Eighteenth year marker 18 years 18 × 360 = 6480 days 6480 → 6+4+8+0 = 18 → 1+8 = 9
    Reign length 12 years 12 × 360 = 4320 days 4320 → 4+3+2+0 = 9
    Total window 18 + 12 = 30 years 6480 + 4320 = 10800 days 10800 → 1+0+8+0+0 = 9

    The regnal math that frames when "the word of the prophet" reaches the king (2 Kings 3) collapses to 9, the Ark dimensions collapse to 9, and the Temple inch-counts collapse to 9.

    Biblical Measures & Times (KJV) — Base-6 + Expanded Time + Root

    Assumptions: 1 cubit = 18 inches = 1.5 ft; prophetic year = 360 days (30-day months). Base-6 uses digits 0-5. "Root" = digital root (sum of digits to 1-9; 0→0).

    Wide reference table — scroll inside or open as overlay.
    Verse Text (KJV excerpt) Original Inches Root Feet Base-6
    of inches / days    		 Expanded Time
    days→hours→minutes→seconds    		 Notes
    Rev 21:17 "...an hundred and forty and four cubits..." 144 cubits 2,592 9 216 20000 - Wall of New Jerusalem; 144 ↔ 216 (6³) resonance.
    Rev 21:16 "...twelve thousand furlongs. The length and the breadth and the height of it are equal." 12,000 furlongs - - - - - Included for the 12 ↔ 144 pairing with v.17 (not cubits).
    Dan 3:1 "...height was threescore cubits, and the breadth thereof six cubits..." 60 × 6 cubits 1,080 × 108 9 × 9 90 × 9 5000 × 300 - Nebuchadnezzar's image; neat 108/1080 patterning.
    Gen 6:15 "...length three hundred cubits, breadth fifty cubits, height thirty cubits." 300 × 50 × 30 c 5,400 × 900 × 540 9 × 9 × 9 450 × 75 × 45 41000 × 4100 × 2300 - Noah's Ark dimensions; recurring /9 digital roots.
    1 Kgs 7:23 "...ten cubits from the one brim to the other... height five cubits... a line of thirty cubits..." D=10 c; h=5 c; C=30 c D=180; h=90; C=540 9 / 9 / 9 D=15; h=7.5; C=45 D=500; h=230; C=2300 - "Molten Sea" in the Temple court.
    Ezek 40:5 "...a measuring reed of six cubits long by the cubit and an hand breadth..." 6 cubits 108 9 9 300 - "Long" cubit noted, harmony still at 6×.
    Prophetic Times (360-day year)
    Rev 11:2 "...tread under foot forty and two months." 42 months 1,260 9 - 110 (42 in base-6) 1,260 d → 30,240 h → 1,814,400 m → 108,864,000 s 42×30 = 1,260 days.
    Rev 11:3; 12:6 "...a thousand two hundred and threescore days." 1,260 days 1,260 9 - 5500 1,260 d → 30,240 h → 1,814,400 m → 108,864,000 s Equivalent to 42 months at 30 days/month.
    Rev 12:14 "...for a time, and times, and half a time..." 3½ years (360-day yr) 1,260 9 - 5500 1,260 d → 30,240 h → 1,814,400 m → 108,864,000 s Same span as above (3.5×360).
    Gen 7:24 "And the waters prevailed... an hundred and fifty days." 150 days 150 6 - 410 150 d → 3,600 h → 216,000 m → 12,960,000 s 5 months × 30-day months in Flood chronology.

    Why base-6? Your sacred-number set (for example 36, 72, 108, 144, 216, 432, 2,592...) compresses cleanly in senary: 2,592 → 20000, 1,080 → 5000, 540 → 2300, 108 → 300, etc.

    Biblical Measures & Times — full table view
    Giants and Iron - Hebrew Cubit (18 in) in Inches and Feet, with Digital Roots
    Og of Bashan - Iron Bedstead (Deuteronomy 3:11)
    Goliath of Gath (1 Samuel 17:4,7) — height and iron spear
    Measure Cubits (common) Conversion (to inches and feet) Inches Feet Digital root (base-10)
    Length 9 9 x 18 in per cubit = 162 in = 13.5 ft 162 in 13.5 ft DR(162)=9
    Width 4 4 x 18 in per cubit = 72 in = 6.0 ft 72 in 6.0 ft DR(72)=9
    Area (rectangular bound) 9 x 4 (9x18) x (4x18) = 162 x 72 = 11664 in^2 = 81.0 ft^2 11664 in^2 81.0 ft^2 DR(11664)=9; DR(81)=9
    Perimeter 2(9+4)=26 2(162+72) = 468 in = 39.0 ft 468 in 39.0 ft DR(468)=9; DR(39)=3
    Item Textual measure Inches / Feet Digital root (base-10)
    Height 6 cubits + 1 span 6*18 + 9 = 117 in = 9 ft 9 in DR(117)=9
    Spearhead (iron) 600 shekels of iron numeric weight figure only DR(600)=6
    Assumptions: Hebrew/common cubit = 18.0 inches; span = 9 inches. Digital root is the iterated sum of digits to one digit. Og's iron bedstead: length 9 cubits, width 4 cubits. Goliath: height 6 cubits and a span; spearhead mass recorded as 600 shekels of iron.
    Additional Dimensions (cubits) — Examples
    Item / Structure Reference Measure (cubits)
    Ark window and roof finish (upper allowance) Genesis 6:16 Finish to a cubit from above
    Tabernacle (overall tent) Exodus 26:15-30 30 x 10 x 10
    Holy Place (within tabernacle) Exodus 26; 26:33-35 20 x 10 x 10
    Curtains (each curtain size) Exodus 26:2 28 x 4 (each)
    Goat-hair curtains (each) Exodus 26:8 30 x 4 (each)
    Boards for tabernacle (height of each) Exodus 26:16 10 high, 1.5 wide (each board)
    Side chambers (three stories, width by story) 1 Kings 6:6 5 (lowest), 6 (middle), 7 (upper)
    Laver stands (each stand) 1 Kings 7:27 4 x 4 x 3
    Outer gate (length x width) Ezekiel 40:21 (also 40:25,29) 50 x 25
    Outer court (square) Ezekiel 40:47 100 x 100; altar before the house
    Temple building (overall length) Ezekiel 41:13 100 (overall length)
    Rear building (width behind temple) Ezekiel 41:14-15 70 wide; 90 long
    Altar hearth (top platform, ariel) Ezekiel 43:15-17 12 x 12; lower ledge 14 x 14; heights in cubits
    Outer wall (separation) Ezekiel 42:20 500 reeds square (note: reeds, not cubits)
    Additional Timelines / Durations — Examples Only
    Event or Period Reference Stated time
    Human lifespan limit statement Genesis 6:3 120 years
    Sojourn prophecy to Abram Genesis 15:13 400 years
    Joseph: years of plenty and famine Genesis 41:29-30 7 years + 7 years
    Ezekiel symbolic days (Israel + Judah) Ezekiel 4:5-6 390 days + 40 days
    Daniel: daily offerings interrupted Daniel 8:14 2300 evenings-mornings
    Daniel: days until blessing Daniel 12:11-12 1290 days; 1335 days
    Jonah in the fish Jonah 1:17 3 days and 3 nights
    Counting to Pentecost (Feast of Weeks) Leviticus 23:15-16 7 weeks complete; 50th day
    Millennial reign (thousand years) Revelation 20:2-7 1000 years
    Reading the Bible with Symbolic Glasses On

    This short note is offered with respect for every reader and their faith practice. It does not try to take anything away. It simply adds a set of glasses that many early readers used: number, pattern, temple imagery, and sky time. With these glasses the text can read less like a child story and more like layered wisdom. Please test every claim for yourself.

    Why these glasses help
    • Older study paths taught arithmetic, geometry, music, and astronomy together. Modern readers often did not get that toolkit.
    • The Bible sits in a temple and calendar world. Without that map, signs flatten into only literal or only myth.
    • Balance matters. The classic fourfold reading held literal, moral, symbolic, and heavenly layers at once.
    How to read without losing depth
    1. Hold the four layers together. Literal (what happened), moral (how to live), symbolic (temple and covenant signs), and anagogical (ultimate hope). No single layer cancels the rest.
    2. Use a simple number glossary. 2 = joining or witness (think two circles crossing, vesica).
      5 = hand, Torah pattern, and proportion steps (phi approx 1.618 shows up in growth tales).
      7 = fullness by cycle (lampstand, days).
      12 = tribes and apostles, a full house for service.
      40 = testing and passage time (desert, flood, mountain).
      70 or 72 = the nations and outward mission.
      144 = 12 x 12 completeness in square form.
      153 = a counted fullness (the catch that says nothing is lost).
    3. Watch the forms. Two circles crossing (vesica) often signals heaven and earth meeting. Bread often signals wisdom or teaching. A mountain, a meal, and ordered groups echo temple service. The temple is a small model of the world.
    4. Ask the first-hearer question. What would a person inside the feast calendar and temple rhythm hear in this scene?
    Example: loaves and fish

    Two fish can point to the vesica shape (two become one space), and five loaves can point to the Torah pattern and growth steps. Twelve baskets left over signals a full Israel made ready to serve. The sign works at the table and at the symbol level.

    A gentle invitation

    Please check the numbers and patterns yourself. My Basecalc page collects simple tables and visuals for this older way of reading: cycles, ratios, and digital roots that keep showing up. If even a small piece makes sense, you now have a tool to read more deeply without giving up the plain sense or your devotion.

    Three Days, Death and Return: A Cross-Cultural Timeline

    Different cultures use a similar pattern: descent, death or loss, then a decisive turn "on the third day" or after a set period. Here is a compact overview.

    Approx. Era Culture Story / Figure 3-day or Death-Return Motif Resonance with Christian "3rd Day"
    c. 2000 BCE Sumerian / Mesopotamian Inanna / Ishtar Descent to the underworld; Inanna is killed and hung on a hook. If she does not return after three days and three nights, the gods are asked to intervene. She is revived and returns, with a substitute sent below. Very explicit "three days and three nights" dead, then restoration. Shows the deep Near Eastern pattern of a god passing through death and returning.
    2nd millennium BCE and later Egypt, Levant, Mesopotamia Osiris, Dumuzi / Tammuz, Baal Gods linked to grain, flood and rain. They die, go to the underworld or are dismembered, then return or live on as lords of the dead. Timing is mostly yearly (seasons), not a fixed three days. Same basic idea of dying and returning, tied to the life cycle of nature. Sets the background for later "dying and rising god" language, but without a strict third-day count.
    1st millennium BCE Greek / Phrygian, later Roman Attis and the spring festival Festival sequence around the spring equinox: ritual mourning and "death" of Attis, followed by a day of joy (Hilaria) when his life or presence is restored. The emotional arc runs over about three days. Death, mourning, then joy at the god's return in the same spring window where Easter later sits. Not word-for-word the same story, but very similar seasonal symbolism.
    c. 1st millennium BCE Israel (Hebrew Bible) "Third day" pattern Several key events happen "on the third day": Abraham and Isaac, Sinai revelation, Hosea 6:2 ("after two days he will revive us, on the third day he will raise us up"). "Third day" becomes a signal for decisive rescue or revelation by God. Provides an internal biblical logic: the third day is when God steps in. This is the main scriptural background used by early Christians for Jesus rising "on the third day."
    Late Second Temple period Jewish Jonah and later beliefs about death Jonah spends three days and three nights in the fish. Later Jewish teaching often says the soul stays near the body for three days before departing for good. Makes three days the threshold of "really dead." A third-day return is not just a short fainting spell, but a true reversal of death.
    1st century CE Early Christianity Jesus: cross, tomb, "rebuild the temple" Jesus predicts he will be raised on the third day and speaks of "destroy this temple and in three days I will raise it up," interpreted as his body. Death at Passover, buried before the Sabbath, discovered alive on the third day. Combines the older Hebrew "third day" rescue pattern with the wider Near Eastern theme of death and return, now focused on one historical person and tied to Passover and the spring equinox window.

    In all these stories you can see the same "cosmic hardware": a three-day threshold for death, and key turning points at solstices, equinoxes and seasonal change. Different traditions install different "mythic software" on that hardware: Inanna, Osiris, Attis, Baal, the Hebrew Bible stories and Jesus all use the same time pattern in their own way.

    Note: 3 days = 72 hours = 4320 minutes = 259200 seconds. The same 72, 432 and 25920 / 259200 number family appears in the precession and harmonic ratios used elsewhere on this page.

    Other Scripture with a 432 Family Relation

    These examples are outside the Bible chapter above, but are still treated here as scripture/tradition entries. The method stays the same: use a literal number found in the text or in the reading/canon structure, then show a clean 432 bridge.

    Torah: Exodus 14:19-21 (72-letter tradition)
    Literal number: 72 (letter-count tradition for each of the 3 verses)
    Bridge: 72 x 6 = 432
    Result: 432
    Tag: letter-count tradition
    Torah structure: 54 weekly portions (parashot)
    Literal number: 54 (annual Torah portion count in the weekly reading cycle)
    Bridge: 54 x 8 = 432
    Result: 432
    Tag: canon/reading structure
    Mishnah: Pirkei Avot 5:21 (age ladder includes 18)
    Literal number: 18
    Bridge: 18 x 24 = 432
    Result: 432
    Tag: literal number in rabbinic text
    Tanakh structure: 24 books (Jewish canon count)
    Literal number: 24
    Bridge: 24 x 18 = 432
    Result: 432
    Tag: canon/reading structure
    Note: The bridges above are simple arithmetic. This section is a "pattern lab" add-on to the Biblical chapter, not a claim of author intent.
    Other scripture with a 432-family relation

    Not "proof" of anything by itself. Just clean numeric hooks that land directly on the 432-family (432, 144, 72, 216, 4320, 432000, 864000, 4320000, etc.) across multiple traditions.

    Satapatha Brahmana / Rigveda syllable-count tradition
    Literal number: 432000
    432 bridge: 432000 = 432 × 1000
    Hook: 432 with zeros (scale-invariant family)
    Puranic yugas (Kali Yuga length)
    Literal number: 432000 years
    432 bridge: 432000 = 432 × 1000
    Hook: "age-length" expressed as 432 with scaling
    Puranic yugas (Maha/Chaturyuga total)
    Literal number: 4320000 years
    432 bridge: 4320000 = 432 × 10000
    Hook: 4320/432000/4320000 ladder
    Poetic Edda (Grimnismal: Valhalla count)
    Literal numbers: 540 doors, 800 warriors each
    432 bridge: 540 × 800 = 432000
    Hook: factor-product lands exactly on 432000
    Torah: Numbers 35:7 (Levitical cities)
    Literal number: 48 cities
    432 bridge: 48 × 9 = 432
    Hook: 48 (structure) × 9 (root-9 amplifier)
    Talmud: Megillah 14a (prophetic count)
    Literal number: 48 prophets (plus 7 prophetesses)
    432 bridge: 48 × 9 = 432
    Hook: same 48 × 9 landing
    Amidah / Shemoneh Esrei (original structure)
    Literal number: 18 blessings (originally)
    432 bridge: 18 × 24 = 432
    Hook: 18 (chai / prayer structure) × 24 (cycle frame)
    Berakhot 28b (daily recitation phrasing)
    Literal number: 18 (the "prayer of eighteen")
    432 bridge: 18 × 24 = 432
    Hook: second independent anchor for the same 18-structure
    Revelation 21:17 (measurement motif)
    Literal number: 144 cubits
    432 bridge: 144 × 3 = 432
    Hook: 144-family (12 x 12) stepped into 432
    Revelation 7:4 (sealed count)
    Literal number: 144000
    432 bridge: 144000 = 144 × 1000, and 144 × 3 = 432
    Hook: 144 core shows again, scaled by zeros
    Note: Some traditions differ by manuscript, translation, or later commentary. Basecalc-friendly approach: keep the literal count as quoted, then show the cleanest factor bridge into the 432 family.

    Harmonic Base Calculator with Harmonic Math Key

    Enter a number, pick a base, then view its conversions and harmonic notes.

    Base Conversion

    Example is 540, which lives in the 3–6–9 family.

    Output & Harmonic Notes

    The calculator shows conversions across bases 6, 9, 10, 12, 24 and 60, plus digital roots and short notes on how each value sits inside the harmonic grid.

    Golden Ratio (phi) Convergence - "Simple Multiplications to Perfection"
    Sacred geometry and flower

    We show three ultra-simple processes that race toward phi ~ 1.6180339887...:

    1. Fibonacci ratios: F(n+1)/F(n) -> phi.
    2. Reciprocal map: x(n+1) = 1 + 1/x(n) (start at 1) -> phi.
    3. Sum-multiplicative ladder: starting from a,b > 0, update (a,b) <- (b, a+b). Ratios b/a -> phi.
    "phi Constant" in phi, Root 9

    Extending phi = 1.618033988749894... through 100 decimal truncations, the digital root (sum of digits -> 1 to 9) returns 9 at specific intervals: 10, 18, 26, 30, 32, 34, 46, 47, 50, 54, 57, 79, 84, 87, 94, 95.

    These positions mirror the same harmonic numbers that resonate through the BaseKalk framework - 432, 369, 396, 234, 144, 108, 54 - repeating as fractal reflections of Root 9 within phi itself.

    Each point where a phi prefix -> Root 9 marks a resonant closure in its decimal spiral, echoing the geometry of precession and the same Mayan / Platonic harmonic structure.

    "A constant" in phi - Root 9 - reveals its own cosmic timing.

    Position phi (truncated) Digital Root Resonant Harmonic
    101.61803398879432
    181.61803398874989489369
    261.61803398874989484829396
    301.61803398874989484820459234
    321.6180339887498948482045869144
    341.618033988749894848204586839108
    461.6180339887498948482045868343656954

    Table 1 - Root-9 intervals within phi - reflections of the Harmonic BaseKalk sequence.

    "phi Constant" in phi, Root 9 - Excluding the 1
    DR = 9 hit (digits after comma) Total Sum up to that digit Digital Root phi fractional prefix (truncated)
    5189.61803
    17999.61803398874989484
    231269.61803398874989484820458
    351809.61803398874989484820458683436563811
    442169.61803398874989484820458683436563811772030917
    452259.618033988749894848204586834365638117720309179
    522619.6180339887498948482045868343656381177203091798057628
    552709.6180339887498948482045868343656381177203091798057628621
    683249.61803398874989484820458683436563811772030917980576286213544862270526
    693249.618033988749894848204586834365638117720309179805762862135448622705260
    964419.618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391

    Table 2 - Constant in phi - Root-9 intervals (excluding the 1) - after-comma cumulative sums where Digital Root = 9.

    After-comma Root-9 in φ: Summing only the digits after the comma of φ and taking the base-10 digital root, the running sum returns to 9 at several positions from the sacred list, most clearly at n = 96, 216, 10240, and at many sexagesimal milestones (for example 720, 960, 1080, 1800, 2304, 2400). These hits cluster on the 3-6-9 / base-6 lattice (multiples of 6, 36, 216 = 6^3), forming a recognizable "after-comma" Root-9 beat.

    Note: Which exact n hits depends on whether we count the leading 1 or not; most hits shift between the two conventions, with only a few shared anchors (96, 216, 10240). Root-9 repeats in both views, but the cleanest alignments tend to sit on the sexagesimal grid.

    The Golden Ratio - "As Above, So Below"

    phi = (1 + sqrt(5)) / 2
    Alternative note: 1 + sqrt(5) leads to phi when divided by 2.

    What the ratio expresses

    Take a whole unity, say 1. Divide it into two parts: a larger part and a smaller part, such that the whole : larger = larger : smaller. That special value is the golden ratio (phi) ~ 1.618.

    In symbols: let the whole = 1, the larger part = a, the smaller part = b. Then 1 : a = a : b -> which yields a/b = a/(1 - a) = phi ~ 1.618.

    Self-similarity => "micro contains macro / macro contains micro"

    When you divide in that ratio, you get a structure that embeds itself: the whole (1) relates to the larger part (~ 0.618 of 1) in the same way the larger part relates to the smaller part.

    The larger part is a scaled-down version of the whole in proportions, and the smaller part is a further scaled version. This gives a nested sequence of proportions: macro contains micro, and micro contains another micro-pattern - "as above, so below."

    Why nature might use it

    In growth, reproduction, and pattern-making (plants, shells, branching, phyllotaxis, and so on), a division or multiplication in the golden ratio lets new growth mirror the proportions of existing structure. Because of the self-similar relation, adding or subdividing in that ratio preserves a harmonic proportion across scale.

    For example: start with size 1. Multiply by phi (~ 1.618) -> ~ 1.618. That new size can then be subdivided so the larger part is ~ 1 and the smaller ~ 0.618, and the proportions map the same way. Each "generation" of growth remains proportionally consistent, preserving form through scale.

    A simple numeric illustration

    Start with 1 -> multiply by phi ~ 1.618 -> whole ~ 1.618.
    Divide in golden ratio: larger ~ 1.000, smaller ~ 0.618.
    Check: larger : smaller ~ 1.000 : 0.618 ~ 1.618 (same ratio).
    Divide the larger part again: larger ~ 0.618, smaller ~ 0.382, and so on.

    Each level replicates the ratio pattern. Because each "part" carries the same proportion as the "whole", the micro-level carries the macro-pattern.

    Plain metaphor

    Imagine a plant branching: the main stem is the "whole", the major branch the "larger part", the minor branch the "smaller part". If the growth splits in golden ratio, the branch-structure keeps the same proportion at each level. Each branch (micro) reflects the form of the trunk (macro). Thus: 1 : 1.618 acts like a "growth-division formula" by which the total remains in the same proportions as it was and will be ("past-present-future in one"). The pattern reproduces itself.

    Fibonacci squares and spiral (5x5, 8x8, 13x13, 21x21)
    Click image to view larger.
    Geometry collage
    Flowers with geometry overlays
    Vesica Piscis - Sacred Intersection of Light and Form
    Vesica Piscis
    153
    Root lengths from two-circle construction

    Vesica Piscis - Sacred Intersection of Light and Form

    1) Pythagoras in one line

    For any right-angled triangle: a2 + b2 = c2
    a and b are the two short sides (the legs).
    c is the longest side (the hypotenuse).
    Kid version: "Square the legs, add them, then take the square root to get the slanted side."

    2) Three tiny recipes for square roots

    √2 - the square's diagonal

    Picture a 1x1 square and draw the diagonal.
    Legs: a = 1, b = 1
    Compute: 12 + 12 = 1 + 1 = 2 → c = √2 (approx. 1.414)
    Kid talk: "One step across and one step up makes a root-two slanted side."

    √3 - the Vesica Piscis height

    Make two unit circles (radius = 1) so each center lies on the other circle. The almond-shaped overlap is the Vesica Piscis.
    Inside it is an equilateral triangle of side 1. Its half-height is:
    height = sqrt(12 - (1/2)2) = sqrt(1 - 1/4) = sqrt(3/4) = √3 / 2
    The full top-to-bottom line in the vesica stacks two of these: (√3 / 2) + (√3 / 2) = √3 (approx. 1.732)
    Kid talk: "In the magic almond, the tall middle is root-three when circles have size 1."

    √5 - the 1x2 rectangle's diagonal

    Draw a 1x2 rectangle and its diagonal.
    Legs: a = 1, b = 2
    Compute: 12 + 22 = 1 + 4 = 5 → c = √5 (approx. 2.236)
    Kid talk: "Go one square across and two squares up; the shortcut is root-five long."

    3) Why this is Ratio 1 magic

    Use unit size (call it "1") as your measuring stick:

    • A 1x1 square gives √2 as its diagonal by a2 + b2 = c2.
    • The Vesica Piscis (two unit circles) hides a side-1 equilateral triangle, so its full vertical span is √3.
    • A simple 1x2 rectangle gives √5 as its diagonal by the same rule.

    In short: divide space with unit shapes and use a2 + b2 = c2, and the square roots appear naturally:
    12 + 12 = 2 → √2   |   1 - (1/2)2 → √3 / 2 → √3   |   12 + 22 = 5 → √5

    4) Do-it-yourself steps (child-friendly)

    1. Choose unit 1. Draw with side or radius = 1.
    2. Make a right triangle (square diagonal, vesica height triangle, or a 1x2 rectangle).
    3. Square, add, root. Write the two leg lengths, square each, add them, then take the square root to get the slanted side or full height.

    Historical note on credit

    Pythagoras (6th century BCE) is widely credited with the theorem a2 + b2 = c2, but the idea is older and appears in several ancient cultures:

    • Mesopotamia (Old Babylonian period, about 1800–1600 BCE): clay tablets (for example, Plimpton 322) list integer triples like 3–4–5 that satisfy the rule.
    • Ancient Egypt (about 1650 BCE): rope-stretchers used the 3–4–5 triangle for right angles in land surveying (Rhind Mathematical Papyrus).
    • Ancient India (about 800–500 BCE): the Sulba Sutras (for example, Baudhayana) state the right-triangle relation and list many triples.
    • Ancient China (compiled about 1st century BCE): the Zhoubi Suanjing explains the Gougu (legs-hypotenuse) theorem, equivalent to a2 + b2 = c2.

    Simple takeaway for kids: Pythagoras made it famous, but builders and scribes across the ancient world already used this right-corner rule to measure land and make things square and true.

    Seed → Egg → Flower of Life Animation
    153, Vesica Piscis & the Seed of Life

    The number 153, often referred to as the "fisherman's number," arises in John 21:11, where the disciples catch 153 large fish after Jesus tells them where to cast their nets. This passage, often mistaken for a miraculous event, is deeply encoded with mathematical and harmonic symbolism — not just literal narrative.

    The harmonic significance of 153 and the Seed of Life
    153 is the 17th triangular number — the sum of all integers from 1 to 17 (1 + 2 + 3 + … + 17 = 153). This is symbolically significant because 17 correlates with the Vesica Piscis geometry, a foundational form from which the Seed of Life emerges. The Seed of Life, constructed from 7 interlocking circles, also relates to musical and harmonic intervals, echoing sacred creation codes.

    The number 153 is also linked to the Vesica Piscis ratio (√3 ≈ 1.732), the square root of 3, through its mathematical properties. When divided by the number of fishers (perhaps 7), the quotient is about 21.857 — close to the mathematical value of 1 / √(1 − φ2) (where φ is the golden ratio), embedding a fractal harmonic into the narrative.

    The feeding of the 5000: symbolic arithmetic
    Jesus feeds a multitude with 2 fish and 5 loaves, and 12 baskets remain full. Here again, the symbolic numerics align with cosmic geometry:

    • 2 + 5 = 7, the number of completion and central to the Seed of Life.
    • 12 is the number of disciples, tribes, and zodiacal houses — symbolizing cosmic governance and harmonic order.
    • The baskets remaining full symbolizes that harmonic sharing multiplies rather than depletes — a principle found in fractal systems and abundance codes.

    This is less about physical multiplication and more about harmonic resonance. When coherence and right alignment are present (as in sharing or faith), the field itself becomes multiplicative, not consumptive.

    Why the net was not torn
    John 21:11 emphasizes that, even with 153 large fish, the net was not torn. Symbolically, the net represents the matrix or fabric of spacetime, or more intimately, the field of connection between individuals. Its integrity remaining intact suggests that unity held under harmonic abundance — a fractal structure can withstand multiplicity without rupture, as long as coherence is preserved.

    Symbolically, it is a message: spiritual networks do not tear when filled with harmonic multiplicity — they grow stronger.

    Vesica Piscis 265 over 153

    Diagram showing the harmonic relationship between 265 and 153 in the Vesica Piscis,
    illustrating that 1 / h = √3 ≈ 265 / 153.

    153 -> 666 : Harmonic Closure of Root Sums

    Summing all digital roots across the full alphabet (A = 1 … Z = 26) and their harmonic extensions (×6, ×9) gives:

    Root Column Σ
    Root(Value)126
    Root(6 × n)153
    Root(9 × n)234
    Total 513

    The combined total of 513 forms a direct harmonic link to the triadic constant 153 — the 17th triangular number (1 + 2 + … + 17 = 153), known since antiquity as the "Fisherman's Number."

    When balanced by its mirror: 513 + 153 = 666, it reveals the same Root 9 closure found throughout Base Kalk's harmonic geometry — the constant resonance of 3 – 6 – 9 within the phi field.

    In essence: 153 completes 666 — the harmonic seal of Root 9.

    Φ Formulas — Exact and Limit Forms
    Formula (exact) Notes Formula (limit)
    φ = (1 + âš5) / 2 Closed form (golden ratio) NaN
    φ = 2 · cos(36°) From pentagon/decagon geometry NaN
    φ^2 = φ + 1 Characteristic quadratic; implies φ = (1 + âš5) / 2 NaN
    1/φ = φ ⒠1 Self‑reciprocal property NaN
    NaN Ratio of consecutive Fibonacci numbers φ = lim_{n→âž} F_{n+1} / F_n
    🌀 Canonical Spiral Systems

    Four self-similar growth patterns that keep showing up in nature, geometry, sound, and cosmic scale: Spiral of Theodorus (right-triangle root steps), Phyllotaxis / Vogel model (sunflower packing at the golden angle), Logarithmic Spiral (r = a·ebθ — shells & galaxies), and a Cymatic / Rose Spiral (r = a·sin(kθ) standing-wave petals).

    1. Spiral of Theodorus
    âš1 → âš10

    Each step adds a new right triangle with one unit side.
    Radius after n steps = âšn. We stop at âš10.

    2. Phyllotaxis / Vogel
    Golden-angle packing

    Seeds placed at θ = n·137.5° and r âť âšn fill space with near-perfect efficiency (sunflower, pinecone).

    3. Logarithmic Spiral
    r = a·ebθ

    Same curve at any scale (self-similar). Seen in nautilus shells, hurricanes, galaxies.

    4. Cymatic / Rose Spiral
    r = a·sin(kθ)

    Standing-wave petals like cymatic resonance plates and 5-fold sacred geometry (k = 5 here).
    Earth Geometry / Sacred Diameter Reference

    The Earth is not a perfect sphere — the equator bulges.
    • Equatorial diameter ≠7,926 miles
    • Polar diameter ≠7,900 miles
    • Difference ≠26 miles
    • A diagonal / tropic-to-tropic style measure ~7,920 miles
    • A perfect sphere with the same surface area as Earth would have diameter ≠7,920 miles, which is often treated as a “sacred number.”

    Earth (oblate): 7,926 mi equator vs 7,900 mi pole → 26 mile difference. The ~7,920 mi slant appears between tropics.
    “Same surface area as Earth” → idealized sphere with diameter ≠7,920 miles (treated as sacred in many number systems).
    🕉 Sakwala Chakraya - "Wheel of the Universe"
    Sakwala Chakraya illustration

    Sakwala Chakraya - Wheel of the Universe

    The Sakwala Chakraya is a shallow rock carving often described as a cosmological map. It is located in Sri Lanka, in the ancient city of Anuradhapura, inside the Ranmasu Uyana gardens. The site sits a short walk from the Isurumuniya temple, near the Tissa Wewa reservoir.

    • Country: Sri Lanka
    • City/Area: Anuradhapura
    • Place: Ranmasu Uyana (near Isurumuniya and Tissa Wewa)

    Core idea

    • The stone encodes time-as-geometry in a sexagesimal (base-60) spirit: vesica-piscis gates, 3-6-9 ladders, and harmonic partitions that resolve into the Great Year = 25920 sacred years (360-day year framing).
    • Numbers like 432, 216, 144, 108, 36 act as phase nodes of that larger cycle.

    Symbol map & harmonic arithmetic

    • 20 border symbols x 22 (cycle-symbols) x 6 = 2640
    • 2640 - 2160 = 480 (with 2160 echoing the Moon diameter motif)
    • 25920 / 480 = 54 -> 54 x 2 = 108 (solar/lunar distance lore)
    • 25920 / 20 = 1296 -> cascade: 1296 / 3 = 432, / 6 = 216, / 9 = 144, / 36 = 36
    • Balances: 72 + 36 = 108, 480 - 360 = 120 (360 deg baseline)

    Vesica layout

    • 9 vesica piscis -> nine portals (1 : sqrt(3) union geometry).
    • Vertical symmetry count: 4 up + 1 center + 4 down = 9.

    Total symbol counts

    • 33 inner (3x3 = 9; 3+3 = 6)
    • 20 outer + 1 center -> 33 + 20 + 1 = 54 (-> 108 when doubled)
    • Optional reading: 32 (exclude center ring) x 20 = 640, 640 x 9 = 5760; 8640 - 5760 = 2880 -> 1440 (folds into the 144-family; 144 cubits / 144000 motif).

    Precessional time (sacred-year lens)

    • Great Year = 25920 sacred years (360-day).
    • Phase nodes:
      • 480 years = 1/54 of 25920 (critical step)
      • 1440 years = 1/18 of 25920 = 2 decans approx 20% of ecliptic (Egyptian 36-decan clock)
      • Time mirrors: 480 hours, 28800 minutes (sexagesimal echoes)

    440 and the base systems

    • 20 x 22 = 440 in base-10.
    • Converting 44010 to base-6 gives 20126 (how the 2012 figure arises from 20x22): repeated division by 6 yields remainders 2,1,0,2 -> reversed as 20126.
    • In base-60, 44010 = 7;2060 (i.e., 7x60 + 20).
    • Keeping 2012 as a symbolic phase marker aligns with the mirror-node motif, while the literal sexagesimal form is 7;20.

    Base-10 <-> Base-60: form vs flow

    • Base-10 = form (measures, matter, commerce).
    • Base-60 = flow (time, angles, sky-temple geometry).
    • Their resonant crossings show up at 432, 216, 144, 108, 36 - numbers the slab foregrounds to fuse geometry, music, and calendrics.

    Reading the stone as a "time-gate mandala"

    • 9 vesicas = nine gates / memory layers.
    • 54 points (33 + 20 + 1) -> 108 when doubled (solar/lunar distance lore).
    • The 1296 fan-out (432 / 216 / 144 / 36) maps fractal phases nested inside the 25920-year envelope.

    One-breath summary

    Base-10 speaks the shape; Base-60 conducts the motion; frequency (for example, 440 Hz -> 20126, 7;2060, and the sacred set 432/144/108) bridges them. Sakwala Chakraya makes the Great Year legible as geometry and audible as harmonic number.

    2012 in Base-6 is a tesseract moment in time, not the end...20x22 (in Base-10) = 440, in Base-60 = 720 (years = 10 degrees precession)

    Star-Gate Cosmogram - reading guide

    The carving reads like a walkable cosmogram. The rim shows a bestial band, a wheel of time. Inside are long rectangular lanes that suggest a calendar or processional route. Repeating cross-in-circle marks act as cycle stations. Two spiral centers (noted as 2 x 7 rings) behave like source and return points. Vesica or fish-like lenses show intersections of paths. A square-with-feet glyph looks like an instruction to walk the plan. Overall flow: rim -> lanes -> spiral -> exit, signalling a cyclic view of time rather than a straight line.

    Motifs and plain-meaning hints
    Motif Likely meaning Pattern hooks
    Outer animal rim Zodiac-like perimeter, procession of time, world-ages band Families 12, 24, 36, 72, 360
    Rectangular lanes inside circle Calendar rows, itinerary fields, processional paths Counts map to base-6, base-12, base-60
    Cross-in-circle nodes Cycle stations or turning points Totals that land on 12, 24, 36, 72, 144, 360
    Two spiral centers (2 x 7 rings) Twin source and return, above/below pairing, great turnings Heptads 7 and 14; octave metaphor 1:2
    Vesica or fish-like lenses Intersection of circles, overlap of realms, balance moments Equinox analogy; 3-6-9 digital-root loops by counts
    Square with feet glyph Earth or temple plan that must be walked (embodied path) 4-in-1 union (square in circle), quartering markers
    What to look for when counting
    • Count rim animals. If 12 are clear, check for quartering into 4 groups of 3, or 3 groups of 4.
    • Count total cross-in-circle nodes. See if totals reduce to 12, 24, 36, 72, 144, 360 families.
    • Verify ring counts in each spiral. 7 and 14 are common heptad patterns.
    • Note any open or broken cycles. These may signal gates for intercalation or ritual reset points.
    • Map the square-with-feet position relative to spirals. It may mark the start or end of the walk.
    Reading paths to test (non-exclusive)
    1. Seasonal or ritual calendar: lanes as months or festivals; nodes as stations; open cycles as reset gates.
    2. Cosmology diagram: rim as constellations, lanes as sky bands, spirals as source and return centers.
    3. Pilgrimage or initiation map: walk the rim, enter a gate, traverse stations, reach center, emerge renewed.
    This guide keeps to observable features only: counts, placements, and simple number families. No projection tricks or forced fits. Add counts beside the image and compare in base-6, base-12, base-60, and digital-root if needed elsewhere on the page.
    Borobudur & Ancient Base-6 Figure
    Borobudur temple from above
    Ancient rock carving with base-6 figure
    Borobudur - geometry at human scale (feet and inches only)
    • Base plan: perfect square, 403 ft 6.5 in x 403 ft 6.5 in (approx 4842.5 in per side).
    • Overall form: 9 stacked levels - 6 square terraces (with 4 circumambulatory galleries) + 3 circular rings, crowned by a central stupa.
    • Height: about 115 ft today; original stack (including the hidden foot) often cited near 138 ft.
    • Circular rings: 3 concentric rings with 72 perforated stupas arranged 32 + 24 + 16 around the great central stupa.
    • Statues and reliefs: 504 seated Buddhas; 2672 narrative relief panels.
    • Geometric language: concentric square->circle mandala, strict axial symmetry, common proportional reading 4 : 6 : 9.
    • Sacred numerics: 72 -> 7+2 = 9 and 504 -> 5+0+4 = 9 (digital-root / base-9 resonance).
    Also shown on the picture above: ancient base-6 headed figure (3x3 = 9, root 9).
    Rock Painting Cosmogram - structure, counts, and possible meanings

    Many so-called primitive panels encode ordered ideas: cosmos layout, cycles, and a walked path. The image here reads as a compact number map: a tree/axis with 12 branches, a cycle sign (circle quartered), a tall 7-headed figure, and groups of 3 small figures. This is consistent with sky observation plus social rite markers rather than random marks.

    Elements and number families
    Element Plain reading Number pattern notes
    Tree with 12 branches Axis mundi or world tree; a vertical link between ground and sky 12 fits months, winds, directions by fours, or zodiac style indexing; pairs well with base-6 and base-60 cycles
    Quartered circle near the tree Cycle sign: fourfold partition of a whole (seasons, quarters, cardinal points) 4 divides 12 (3 per season); typical for solstice and equinox mapping
    Seven-headed tall figure Composite or crowned person; completeness marker across the seven layers/heavens Heptad set: 7 days, 7 classical planets, 7 heavens; in music an octave frame touches 7 named steps before the 8th return
    Three small figures in a cluster Procession or lineage; triad unit used for counting or ritual grouping Triads stack to 9 (digital root 9 motif); 3 x 4 = 12 links to the tree count above
    Repeated vertical strokes and side glyphs Tallies or clan marks; could be step counts on an initiation route Look for totals that land on 12, 24, 36, 72, or 144 for calendar math; check digital roots
    How the parts can work together
    • The tree/axis provides the vertical order. Twelve branches distribute the cycle horizontally.
    • The quartered circle fixes the four turning points so the 12 can be read as 4 x 3 or 3 x 4.
    • The 7-headed figure marks completeness or mastery across seven levels. Read as ascent or initiation.
    • The triad of small figures preserves the 3 that builds 6 and 12, and collapses to digital root 9 when summed in groups.
    • Together this forms a compact calendar-cosmology-ritual map: count, walk, return.
    Why this is far from primitive

    The panel combines an axis, a fourfold cycle, a sevenfold completeness sign, and a twelvefold distribution. Those are standard building blocks of measured time and sacred space across many cultures. When counts from the same panel coherently map to base-6, base-12, and base-60 families, the intent is mathematical and cosmological, not random decoration.

    Note: exact meanings depend on site, date, and tradition. The reading above stays with observable counts and widely attested number families (7, 12, 4, and triads). It can be compared alongside other cosmograms such as temple terraces, zodiac bands, and processional calendars without forcing a one-to-one identity.
    Samarra Bowl - origin, motifs, and counted structure
    Samarra bowl, c. 4000 BCE, Mesopotamia
    Samarra bowl (earthenware), c. 4000 BCE, Mesopotamia. Excavated at Samarra (present-day Iraq) by Ernst Herzfeld.
    Origin and context

    Earthenware bowl from Samarra, present-day Iraq, dated around 4000 BCE. The piece is associated with the Samarra or early Mesopotamian cultural horizon and was excavated by the German archaeologist Ernst Herzfeld.

    What is depicted
    • A woven or meander rim that runs around the plate.
    • A ring of eight fish arranged around the field.
    • Four birds, each shown catching a fish, dividing the circle into four sectors.
    • A whirling cross at the center (ancient rotation or solar emblem), giving a spinning or vortex effect to the design.
    Counted structure and number notes
    Element Count / relation Reading
    Fish total 8 outer + 4 inner (via birds) = 12 Twelve-unit set (months or zodiac-style enumeration); DR(12)=3
    Radial dividers 4 sectors Quartering of the circle (seasons or directions). 12 = 4 x 3.
    Central hub Whirling cross Axis and rotation marker; visually drives the four quarters.
    Perimeter band Continuous meander Net or circuit that closes the cycle; reads as a counting path around the rim.
    Synthesis

    The bowl composes a measured cosmos: a rotating hub, four seasonal gates, and twelve counted creatures within a continuous perimeter. From a Mesopotamian perspective the fish and birds are apt symbols for riverine life and annual cycles, while the quartering and the twelvefold set show a practical way to encode time on a domestic ritual object.

    Golden Ratio & Human Proportions

    Definition (Golden Section)

    A segment is divided in the golden ratio when the ratio of the whole to the larger part equals the ratio of the larger part to the smaller part.
    (a + b) / b = b / a = φ
    ⇒ a<sup>2</sup> + a b − b<sup>2</sup> = 0
    ⇒ (a/b)<sup>2</sup> + (a/b) − 1 = 0
    ⇒ a/b = φ<sup>−1</sup> = (√5 − 1) / 2 ≈ 0.618034
    ⇒ φ = (1 + √5) / 2 ≈ 1.618034
    Rasart modular strip - human measurements (wide)

    Worked Example

    Take a person of height 192.5 cm. Golden ratio partitions of the height fall at the following levels:

    LevelCentimeters
    Total height (H)192.50
    Navel level (H/φ)118.97
    Solar / diaphragm region (H/φ<sup>2</sup>)73.53
    Knee region (H/φ<sup>3</sup>)45.44
    Mid shin / ankle region (H/φ<sup>4</sup>)28.09

    These are guidelines; individual anatomy varies.

    Personal Proportions Tool

    Enter your total height and get the corresponding landmarks based on the Rasart phi scheme (navel approx H/φ, knee approx H/φ<sup>2</sup>, fingertips (arm raised) approx 2 * H/φ). Values are shown in centimeters / millimeters and feet inches.

    Current: 192.5 cm


    Landmark Exact (cm) Nearest whole cm Delta (mm) Feet Inches
    Total height (H)————
    Navel height (H/φ)————
    Knee height (H/φ<sup>2</sup>)————
    Fingertips, arm raised (2 * H/φ)————

    φ = (1 + √5) / 2 ≈ 1.618033988. These are canonical guides; real anatomy varies.

    Golden Ratio Cascade (times phi / divide phi)

    The table shows the geometric progression around H by powers of phi. Positive n multiplies by phi, negative n divides by phi.

    Vitruvian Man - Hidden Triangle

    Da Vinci Vitruvian Man with hidden triangle overlay
    Star of David guide derived from the Vitruvian framing

    The fact that the difference between the positive and the negative root is minus 1 has a curious meaning. For a rectangle with length 1.618... and width 1: if you place a square along the length with a side equal to the width, the remaining rectangle has the same proportions (length 1.618... and width 1), repeating ad infinitum.

    Golden Ratio study.
    0 ≡ ∞   "Scale is a circle; ends are one."
    1. Boundary identification (one-point compactification):
      $$ (0,\infty)^{*} = (0,\infty) \cup \{\omega\},\quad \lim_{r \to 0^{+}} r = \lim_{r \to \infty} r = \omega,\quad \boxed{0 \equiv \infty}. $$
    2. Equivalence-class statement (quotient = circle of scales):
      $$ [0,\infty]/(0 \sim \infty) \cong S^{1},\qquad \boxed{0 =_{\text{quot}} \infty}. $$
    3. Inversion duality (extended line):
      $$ x \mapsto \frac{1}{x} \ \text{on}\ \overline{\mathbb{R}} \ \Rightarrow\ \boxed{0 \leftrightarrow \infty}. $$

    "Infinitely small" (No-thing) and "infinitely large" (All) coincide by the chosen identification on scale.

    Bisecting a 360° Circle: How Angles Reduce to 9
    A pattern develops when bisecting a circle, The resulting angle always reduces to 9 converging into a singularity. Conversely, the polygons reveal the exact opposite, Their vectors communicate an outward divergence.
    Geometric divergence construction inside a circle
    Geometric divergence construction inside a circle
    The 9 reveals a linear duality, It's both the singularity and the vacuum. 9 models "every"thing and "no"thing simultaneously. Paradoxically, 9 + any digit returns the same digit: (6+9=15, 1+5=6, 3+9=12, 1+2=3, 4+9=13, 1+3=4, etc.) [1+2+3+4+5+6+7+8 = 36 3+6 = 9] So 9 quite literally equals all the digits (36), and nothing (0).
    0 +9 -9 8 1 7 2 5 4 -6 +6 -3 +3
    Dual vortex flow through apple-core torus
    Dual spiral flow above and below the horizon
    9, 1 and 0: potential, paradox and the digit cycles

    So 9 closes the 1-8 cycle (36 -> 9), but behind it stand 1 and 0: 1 as all possible potential (the One), and 0 as the field of potential itself. Zero is not nothing; it is a no-thing state in two directions: both the not-yet-manifest potential and the state that manifested potential returns to. In base 10 that visible cycle is 1-9, while other bases (6, 12, 60, etc.) run their own digit cycles - all still expressions of that same 1 (pure potential) and 0 (the potential field that can become, and the manifested potential that ultimately returns back into the One). The rest of the numbers are just infinite players moving between these two states. In base 10, the 9 reveals this duality - the paradox of this singularity.

    • 0_pre = the not-yet-manifest potential (the "no-thing" state before any digit appears).
    • 1 = all possible potential (the One) from which the digit sequence 2, 3, ..., 8 unfolds.
    • 2 ... 8 = the "infinite players" moving between 0 and 1, the visible steps of manifestation.
    • 9 = the closure of the 1-8 sum (36 -> 9) in base 10, and, at the digital-root level, the gate back to 0 (9 behaves like 0 mod 9).
    • 0_post = the state that manifested potential returns to: the same potential field as 0_pre, now carrying everything back into the One.
    0, 1 and 9 - potential, paradox and the digit cycle
    0_pre as not-yet-manifest potential, 1 as all possible potential (the One), digits 2...8 as infinite players between, 9 as the closure of the 1-8 cycle (36 -> 9) behaving like 0 mod 9, and 0_post as the return state of all manifested potential.
    Infinite inside infinite

    The story of 0, 1 and 9 sits on top of something even more strange: infinity. An infinite set is not just "very big" – it can contain an infinite subset that is the same "size". The classic example is Hilbert's Hotel: a hotel with infinitely many rooms can still make room for new guests by re-numbering the rooms.

    The natural numbers 1,2,3,... and the even numbers 2,4,6,... are both infinite, and there is a perfect pairing 1 -> 2, 2 -> 4, 3 -> 6, in general n -> 2n. So an infinite "whole" can contain an infinite "part" that is the same size. That is one layer of infinity.

    A second layer appears when you look at all real numbers between 0 and 1. There are infinitely many points in that interval, and in any smaller interval inside it. This infinity is strictly "larger" than the infinity of 1,2,3,...: the line [0,1] is a model of a continuous potential field. 

    |N| = |Z| = |Q| = aleph_0      (countable infinity)
|R| = 2^(aleph_0)              (uncountable, larger infinity)

    Seen this way, 1 stands for all possible potential, 0 for the potential field itself, and the visible digits (1-9 in base 10, or the cycles in base 6, 12, 60) are just countable "players" sampling an underlying continuum. Even within infinite there is more infinite: subsets that are still infinite, and whole fields (like [0,1]) whose infinity is larger than the counting numbers that try to name it.

    Primes in the 0 / 1 / 9 field

    0 and 1 set the field of potential, 9 closes the visible cycle in base 10, and primes are the irreducible steps scattered through that infinite field. A prime is only divisible by 1 and itself, so it behaves like an atomic "letter" in the number language: all composite numbers are words built from these prime letters.

    • In digital-root terms, primes greater than 3 never land on 3, 6 or 9: if a number has digital root 3, 6 or 9 it is divisible by 3 and cannot be prime (except 3 itself). So most primes orbit around the 3-6-9 ladder instead of sitting directly on it.
    • In base 6, any prime p > 3 must be of the form 6k+1 or 6k-1. It cannot be 0, 2, 3 or 4 modulo 6 without becoming divisible by 2 or 3. So primes greater than 3 sit just off the pure 6-multiples, like off-beat pulses around a 6-based rhythm.
    • The set of primes is infinite, but it is a "thin" infinity inside the infinity of all natural numbers. They are the irreducible moves that structure the whole field between 0 and infinity, while 0 and 1 mark the potential field itself and 9 seals the base-10 cycle at the digital-root level.
    Prime records: infinite field, but a current "high score"

    Mathematically there are infinitely many primes. Euclid already proved that for any prime you name, you can always build a larger one, so there is no "last" prime and no finite count of how many primes exist.

    In practice we only know a finite subset of this infinite field. Computers keep pushing the frontier upward, so the record changes over time. At the moment, the largest known prime is a Mersenne prime of the form 2^p - 1: 

    Current record (2024):    2^136279841 - 1
Digits in base 10:        41,024,320
Found by:                 GIMPS (Great Internet Mersenne Prime Search)
Discovery date:           12 October 2024

    This "high score" lives inside the same infinite set of primes that begins with 2, 3, 5, 7, 11, 13, ... . The set of primes itself has no upper bound: we can always go further. What changes is only how far human tools have climbed into that infinite landscape so far.

    Digital roots of primes and the 3-6-9 resonance

    In base 10, the digital root dr(n) is just n reduced to a single digit by summing its digits (which is the same as working mod 9 but written as 1..9). Any number with digital root 3, 6 or 9 is divisible by 3.

    For primes this has a sharp consequence: the prime 3 itself has dr(3) = 3, but every prime greater than 3 must avoid the 3-6-9 slots. So for all primes p > 3: 

    dr(p) is always in {1,2,4,5,7,8}, never in {3,6,9}.

    You can think of 3-6-9 as an inner "resonant" track. Binary doubling and primes both run on the outer ring of 6 positions: 1,2,4,5,7,8. The powers of 2 (2^k) move through these in a perfect loop mod 9: 

    2^k mod 9:  1 -> 2 -> 4 -> 8 -> 7 -> 5 -> (back to 1) ...

    After the prime 3, you only see digital roots {1,2,4,5,7,8}, but the order does not repeat in a simple 6-step loop the way doubling does. The primes jump around these six slots in a pattern that, as far as we know, behaves "pseudo-randomly" among them (subject to deeper constraints from prime distribution). In that sense, doubling traces a clean rhythm on the outer ring, while primes appear there like sparks.

    Vortex pattern: 3-6-9 axis and the prime / doubling ring

    Many "vortex math" diagrams are just arithmetic mod 9 drawn on a circle. You take any number, reduce it to a single digit by summing the digits (digital root), and then place that digit on a 1..9 circle. Certain sequences, like doubling, trace simple loops on that circle.

    The famous vortex loop comes from powers of 2 mod 9: 

    2^k mod 9:  1 -> 2 -> 4 -> 8 -> 7 -> 5 -> (back to 1) ...

    This loop lives on the six positions {1,2,4,5,7,8}. The remaining digits 3,6 and 9 form an "inner" track: numbers with digital root 3, 6 or 9 are all divisible by 3. So vortex math naturally splits the 1..9 circle into:

    • an inner 3-6-9 resonance axis (multiples of 3), and
    • an outer ring 1-2-4-5-7-8 visited by the doubling cycle.
    Vortex pattern with inner 3-6-9 and outer 1-2-4-8-7-5
    Inner triangle: 3-6-9 resonance axis. Outer ring: 1-2-4-8-7-5 doubling cycle mod 9. All primes > 3 land only on the outer ring (digital roots in {1,2,4,5,7,8}); prime 3 is the only one sitting directly on the 3-6-9 track.

    When you look at primes through this lens, something clean appears: the prime 3 itself has digital root 3, but every prime p > 3 must avoid the 3-6-9 slots (otherwise it would be divisible by 3). So for all primes p > 3: 

    dr(p) is always in {1,2,4,5,7,8}, never in {3,6,9}.

    In other words: 3-6-9 are the inner "resonant" track. Binary doubling and primes both run on the outer ring of 6 positions {1,2,4,5,7,8}. Doubling runs there in a perfect loop (1 -> 2 -> 4 -> 8 -> 7 -> 5 -> 1 ...), while primes appear on the same ring like sparks: after 3 you only see digital roots {1,2,4,5,7,8}, but the order does not repeat in a simple 6-step pattern. It jumps around in a way that, as far as we know, behaves pseudo-randomly, with deeper structure hidden in the prime distribution.

    3, 9, singularity and the triangle

    In digital-root arithmetic (mod 9), 9 behaves like 0: any number that sums to 9 is congruent to 0 mod 9. At the same time, 9 is the closure of the visible digit cycle, since 1+2+3+4+5+6+7+8 = 36 and 3+6 = 9. In this sense 9 is both the singularity (all digits summed) and the vacuum (the same role as 0 in mod 9).

    The number 9 is 3^2, so 3 can be seen as a root harmonic: the prime that generates the 3-6-9 ladder. In a 360 degree circle, 

    360 = 2^3 × 3^2 × 5
          ?
         3^2 = 9

    so the factor 3^2 is built into the standard circle division. Splits such as 3, 6, 9 and 12 all carry a 3-factor somewhere, which matches the 3-6-9 resonance seen in digital roots and vortex patterns.

    Geometric side: why 3 feels like a "trinity"

    Geometrically, the triangle is the first shape that defines a plane: 3 points, 3 edges. It is the minimal stable 2D structure. That is one reason a "trinity" or triad shows up as a strong archetype in many traditions: 3 is literally the first stable form that can hold a field.

    In this symbolic language:

    • 1 = undivided, pure unity;
    • 2 = split or polarity (two poles of the same field);
    • 3 = first balanced structure that holds both poles together.

    This can be summarised in the phrase "from 1 comes the 3, 3 stays 1". One way to read this is:

    • 1 = pure potential (undivided field),
    • 3 = that potential expressed as a minimal stable pattern (triangle / trinity).

    The pattern is still "one thing", but now internally structured. The 3 does not cancel the 1; it is the 1 showing itself as a stable form.

    3 as root, 9 as closure

    In this view, 3 is the root prime that generates the 3-6-9 ladder and the first stable geometric structure (the triangle), while 9 = 3^2 acts as the closure of the digit cycle and, in mod 9, plays the role of 0. From 1 (pure potential) comes 3 (first stable pattern), and 3^2 closes the loop as 9: a singularity that also behaves like a vacuum, returning the cycle back to the field.

    As a closing note: everything that unfolds from ratio 1 can be seen as a fractal of that One ratio — infinitely large and infinitely fine. Some expressions move "outward" (expansion, external structures), others move "inward" (contraction, internal patterns), but all remain echoes of the same undivided source.
    Dimensions as Harmonic Layers (0D - 12D)

    Each dimension can be read as a standing wave layer: potential, line, plane, volume, and then fields that phase, mirror, store and unify those patterns. The graphic below is animated; watch how the layers breathe and move.

    Dimensions as Harmonic Layers (0D - 12D) - each row shows the basic wave or shape plus a short description.

    DIMENSIONS AS HARMONIC LAYERS

    0D to 12D - standing waves, phase and fields

    Dim Name Plain meaning
    0D Null node Pure potential, no extension; point of infinite compression.
    1D Linear wave Single line of propagation; fundamental tone, monotonic and directional.
    2D Radial projection Plane or membrane from crossing 1D waves.
    3D Spatial volume Enclosed space from resonant planes.
    4D Time as phase rotation 3D volume spinning through phase; history as rotation, not an external axis.
    5D Harmonic polarity field Wave inversion, synchronization and conscious modulation.
    6D Reflective mirror symmetry Mirror field; entangled patterns across scales, inner and outer.
    7D Scalar causality Pre-time causal gradients; layer behind synchronicity and cause-before-time.
    8D Harmonic memory field Resonant storage and replay of waveform sequences; memory as a field.
    9D Light-body template Phase-coherent light geometry that templates form; holographic body field.
    10D Monad field Unity octave where all prior dimensions stand together as one field.
    11D Oversoul field Multi-dimensional observer; not bound to form, synchronizing many timelines.
    12D Source / singularity Seed of the stack; consciousness unfractured, before any differentiation of layers.

    Precession & Sunrises (Northern Hemisphere)

    Precession (big picture): Earth’s spin axis slowly traces a cone because the Sun and Moon torque the equatorial bulge. Rate ≈ 50.3″/year → one full cycle in ~25,772 years (often rounded to 25,920 ≈ 1° per 72 years). The equinox points drift westward along the ecliptic, so the background zodiac constellations behind the equinoxes/solstices change over millennia.

    • Vernal (March) equinox currently lies in Pisces (moving toward Aquarius).
    • September equinox is in Virgo.
    • Solstitial longitudes are in/near Gemini (June) and Sagittarius/Ophiuchus (December).

    Sunrise directions through the year

    Let latitude be φ; Earth’s axial tilt (obliquity) ≈ 23.44°.

    Event Solar declination δ Sunrise (N hemi) Day length Notes
    March & September Equinox 0° Due East; sets due West ≈ 12 h / 12 h “Equal night” (small variations from refraction/latitude)
    June (Summer) Solstice +23.44° North–East; sets North–West Longest day Tropic of Cancer overhead Sun; midnight sun above Arctic Circle
    December (Winter) Solstice −23.44° South–East; sets South–West Shortest day Polar night above Arctic Circle
    Sunrise azimuth approximation

    Azimuth A measured from North (East = 90°). At δ = 0° (equinox), A = 90° (due East). Positive δ (summer) shifts sunrise north of East; negative δ (winter) shifts it south of East.

    Sunrise Azimuths by Latitude (Northern Hemisphere)

    or

    Azimuth is measured from North, clockwise. East = 90°. Dates shown are for 2025.

    Event Date (2025) Solar declination Sunrise azimuth Comment
    June (Summer) Solstice Jun 21 +23.44° -- --
    March Equinox Mar 20 0° -- --
    September Equinox Sep 22 0° -- --
    December (Winter) Solstice Dec 21 −23.44° -- --
    Method

    We use cos A = sin δ / cos φ, where A is azimuth from North, δ is solar declination, and φ is latitude. If |sin δ/cos φ| > 1, sunrise does not occur (midnight sun or polar night).

    Earth Orbit Diagram

    Loading…

    Glossary of Terms

    Short explanations of the most important words used on this page.

    432 Hz
    A musical tuning where the note A is set to 432 vibrations per second.
    Root-9 / Digital Root
    Reducing a number to one digit by adding its digits. Example: 432 -> 4+3+2 = 9.
    Base-10
    The normal number system we use every day (0-9).
    Base-60
    Older counting system that goes 0-59. Used in time (60 seconds, 60 minutes) and angles (360 degrees).
    Precession
    Earth's slow wobble. One full cycle takes about 26000 years (often rounded to 25920).
    Equinox
    The 2 days in the year when day and night are equal length everywhere on Earth.
    Solstice
    The longest and shortest days of the year.
    Phi / Golden Ratio
    A special proportion written as 1.618... found in shells, art, and nature.
    Platonic Solids
    5 perfect 3D shapes: cube, tetrahedron, octahedron, dodecahedron, icosahedron.
    Vesica Piscis
    Shape made by overlapping 2 circles so their centers touch.
    Seed of Life
    Pattern made from 7 circles. Used in many symbols and mandalas.
    Flower of Life
    Repeating geometric pattern based on the Seed of Life.
    Metatron's Cube
    Made from 13 circles and connecting lines. Holds all 5 Platonic solids inside it.
    Harmonics
    Frequencies that are simple multiples of each other, like 432, 864, 216.
    Frequency
    How many times something repeats in 1 second.
    Cycle
    Something that repeats, like seasons, waves, breath, music, orbits.
    Ratio / Proportion
    A comparison of values, like 2:1 or 3:2.
    Sacred Geometry
    The study of shapes and patterns believed to reflect natural order.
    Yuga Cycle
    Very long repeating ages of time described in ancient India.
    Decan
    One of 36 divisions of the zodiac sky, each 10 degrees wide.
    Base Conversion
    Changing a number from one base (like 10) to another (like 6).
    Resonance
    When two vibrating things match in frequency and amplify each other.
    Three life signs: Hopi lifepath, Egyptian ankh, Japanese life character style
    From left to right: a Hopi lifepath motif, the Egyptian ankh, and an old-style Japanese life character form. All three share a loop + cross + stem layout.
    Loop + Cross + Stem "Life" Signs - comparative note

    Three cultures use a very similar graphic recipe to signal life: a loop above a crossbar on a vertical stem. This look-alike outcome can arise in two ways: 1) convergent design from shared human metaphors (head, arms, spine; or bud on a stem crossing the ground line), and 2) cultural transmission along trade routes in parts of the Old World. For the New World case (Hopi), mainstream history sees independent invention; for Egypt and East Asia some long-range style echo is possible, but the forms also make sense as separate solutions to the same idea.

    Culture Name / family Plain meaning Form logic Notes
    Hopi Lifepath / emergence motif Life, journey, emergence Loop as head or seed; vertical path; cross-step marks for walked world Petroglyph tradition of the American Southwest; not a phonetic script
    Egypt Ankh Life, vitality Head loop over staff and crossbar; also read as a strap or knot Part of a full hieroglyphic system with known phonetic values
    Japan / China Life character lineage (Chinese "sheng", Japanese "sei") Life, to grow, living Ancient graph shows a sprout rising through a ground line; later scripts keep the schema East Asian writing family; independent of Egyptian script
    Synthesis

    The shared loop + cross + stem layout compresses a stable triad: head or bud (loop), world line (crossbar), and life axis (vertical). It naturally supports quartering and directional ideas used across base-6, base-12, and base-60 schemes. Similar shapes do not automatically prove direct contact; they do show how a small set of strokes and universal metaphors guide symbol design across distant cultures.

    Notice the universal number families (3, 4, 7, 12) to illustrate how simple geometry and shared embodiment produce parallel symbols.
    Cross and Tau (T): the same skeleton as the looped life signs

    The Christian cross uses the same orthogonal skeleton as the looped life signs (ankh and related forms) - it is the same figure without the loop on top. Reduced to its essence, the symbol is a T (the Tau cross): a vertical axis meeting a horizontal axis at right angles. In universal geometric terms this is the point where two ways intersect - the upright (axis, ascent) and the horizon (world line, spread).

    Minimal elements
    Proportion facts (no speculation)
    Why the forms align across cultures

    The orthogonal cross/T and the looped-top variant speak the same geometric language: vertical axis, horizontal world line, and optional loop. Over time, cultural meanings diverged, but the underlying construction - axes meeting at right angles, sometimes crowned with a loop - remains constant and readable without words.

    Summary: Cross = loopless ankh. Tau (T) is the essential intersection. Set lengths along the arms and the same T carries any exact ratio, including the golden cut when used as the seam of a golden rectangle. The geometry is shared; later meanings drifted.
    Quartered Circle with Four Dots - meaning and uses
    Quartered circle with four dots (Hopi earth symbol style)
    Circle = world or cycle. Cross = north-south and east-west. Four dots = four quarters.
    Hopi reading (earth symbol / shield)
    Related traditions (same geometry, local meanings)
    Why this motif persists

    It is minimal geometry that anyone can read without words: a boundary (circle), orientation (cross), and fourfold balance (dots). It scales from calendar and compass to village plan and moral teaching, which is why it appears in pottery, textiles, flags, plazas, and ritual diagrams across cultures and into the present.

    Sacred Architecture: Knowledge in Stone
    Click a line to jump into the matching tool. Key numbers are shown in gold so you can see how stone, measure and harmony are connected.
    Great Pyramid of Giza, 432 6 family
    Great Pyramid – 432/6 family, height about 280 royal cubits, base about 440 cubits.
    Borobudur temple, Java
    Borobudur – 5 square terraces, 3 circular terraces, about 432 Buddhas and 72 stupas: the same harmonic family as the tables.
    Parthenon facade, Athens
    Parthenon – facade ratio about 4:9, with 8 × 17 columns and a human scale around 1.6 to 1.7 m.
    More Sacred Architecture: Paths of Light
    Three more sites where number, orientation and human movement are written into the stone. Click a line to send their key numbers into the matching tool.
    Chartres Cathedral labyrinth in the nave
    Chartres Cathedral – floor labyrinth with 11 circuits in a circle about 12.9 m across, a 6-petal center and a full path of roughly 260 m.
    Angkor Wat temple at sunrise
    Angkor Wat – temple-mountain with 5 main towers, gallery counts built around 72 and 108, aligned to the rising sun.
    Dome of the Rock, Jerusalem
    Dome of the Rock – an 8-sided plan (octagon) carrying a circular dome: square, octagon and circle stacked as earth, transition and heaven.
    More Sacred Sites: Geometry, Time and Light
    Five more places where numbers and sky cycles are built into stone. Click a line to send their key number or latitude into the matching tool.
    Luxor or Karnak temple colonnade at night
    Luxor / Karnak – long axial temples with processional route and colonnades, aligned with Nile and sky.
    El Castillo pyramid at Chichen Itza
    El Castillo, Chichen Itza – four stairways of 91 steps plus platform: 365 days encoded in stone.
    West facade of Notre-Dame de Paris
    Notre-Dame de Paris – a facade built from simple rectangles and a clear 3-4-7 rhythm in levels and openings.
    Courtyard and minaret of the Great Mosque of Kairouan
    Great Mosque of Kairouan – courtyard, prayer hall and minaret laid out in clean rectangles related by simple ratios.
    Taj Mahal with reflection pool
    Taj Mahal – central tomb and four minarets mirrored in a long garden axis and reflection pool.
    Modern Architects of Proportion
    Sacred geometry did not stop with temples and cathedrals. Some modern architects turned proportions into a conscious "code" again. These examples link their work back into Basecalc and the Human Proportions tool.
    Le Corbusier Modulor diagram
    Le Corbusier – Modulor chart tying a 1.83 m man to a phi-based ladder of measures.
    Farnsworth House by Mies van der Rohe
    Mies van der Rohe – Farnsworth House: a glass box with very clear, almost "pure" rectangle ratios.
    Mario Botta San Giovanni Battista church interior
    Mario Botta – San Giovanni Battista: stripes, cylinders and an elliptical shell cut by a circular roof opening.
    Sagrada Familia towers by Antoni Gaudi
    Antoni Gaudi – Sagrada Familia: branching columns and up to 18 towers planned in a vertical "score" of stone.
    Louvre glass pyramid at night by I. M. Pei
    I. M. Pei – Louvre Pyramid: a glass pyramid with a slope near 51.5°, echoing ancient pyramid geometry.
    Santiago Calatrava bridge with repeating ribs
    Santiago Calatrava – bridge with repeating ribs: structure as a visible rhythm in space.
    Eiffel Tower illuminated at night
    Eiffel Tower, Paris – iron lattice tower with a total height of about 324 m (including antennas), built as the gateway for the 1889 Exposition Universelle.
    🎨 Paintings: Knowledge on Canvas

    Click a line to send its key number into the calculator. Gold numbers mark dimensions, counts or ratios that echo harmonic tables (3–6–9, 432-family, golden ratio and so on). Images open larger when you click them.

    Leonardo da Vinci, Mona Lisa
    Leonardo da Vinci, Mona Lisa – often read as a field of golden rectangles and a φ-spiral through the face and folded hands: a single "one" (monad) seated inside a quiet, harmonic space rather than tied to tape-measure units.
    Leonardo da Vinci, The Last Supper
    Leonardo da Vinci, The Last Supper – count the structure: 3 bands × 8 wall fields × 36 ceiling coffers = 864, with 12 apostles grouped in threes around the central triangle.
    Sandro Botticelli, The Birth of Venus
    Sandro Botticelli, The Birth of Venus – a textbook golden-ratio composition: the shoreline, shell and figure can be framed with nested φ-rectangles and a spiral. The focus is on proportion and placement of the goddess in the field, not on tape-measure units.
    Raphael, The School of Athens
    Raphael, The School of Athens – a hall of geometry and philosophy built from three great arches and, above, a window divided into three parts by columns. The scene is gridded by hidden triangles and converging lines so the eye keeps returning to the central pair. The repeating 3 encodes a root-9 rhythm rather than a random wall size.
    Piet Mondrian, Composition with Red, Blue and Yellow
    Piet Mondrian, Composition with Red, Blue and Yellow – square around 45 cm a side, pure verticals, horizontals and primaries searching for perfect balance.
    Salvador Dali, Soft Watch at the Moment of First Explosion
    Salvador Dalí, Soft Watch at the Moment of First Explosion – a melting clock blown apart in mid-air. The darkened 5 sits in shadow while shards and drops fly out of that sector and a butterfly rests on the rim: the 5 / phi ratio as a fragile shadow of the One, time cracking so transformation (metamorphosis) can enter.
    Salvador Dali, The Sacrament of the Last Supper
    Salvador Dali, The Sacrament of the Last Supper – the scene set inside a transparent dodecahedron (12 pentagonal faces) and framed by a golden rectangle, turning the Last Supper into a conscious φ-geometry meditation.
    Bottom image 1
    Bottom image 2
    3-9-6 harmonic cycle animation