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Chakra · 2D · v1.0.0

Sacral Chakra — Svadhisthana

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P0P1P2P3P4P5P6P7

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Mathematics

Geometric construction

Central circle of radius R; 6 touching petal circles of radius R/2 centred on it; a crescent formed by an inner circle of radius R/2 at the centre and a circle of radius R/2 centred at (0, R/4).

Symmetry: Mirror symmetry about the vertical axis (petals alone are D6).

Culture

Symbolic interpretation

Six-petalled lotus with a crescent moon, associated with water and creativity. Experimental chakra-inspired construction defined in this product; traditional chakra iconography varies and this is one reproducible reading of it.

Formulas

Available frequency mappings

  • A · Direct ratio fᵢ = f₀ · rᵢ
  • B · Power fᵢ = f₀ · rᵢ^α
  • C · Logarithmic fᵢ = f₀ · 2^(k · log₂ rᵢ)
  • D · Reference distance fᵢ = f₀ · (dᵢ / d_ref)^α
  • E · Angular rᵢ = θᵢ / θ_ref ; fᵢ = f₀ · rᵢ^α
Units u

Coordinates

idxyz
P00.00000.00000.0000
P10.00001.00000.0000
P2-0.86600.50000.0000
P3-0.8660-0.50000.0000
P4-0.0000-1.00000.0000
P50.8660-0.50000.0000
P60.86600.50000.0000
P70.00000.25000.0000

Distances & angles

r(C0)1.0000 u
r(C1)0.5000 u
r(C2)0.5000 u
r(C3)0.5000 u
r(C4)0.5000 u
r(C5)0.5000 u
r(C6)0.5000 u
r(C7)0.5000 u
r(C8)0.5000 u
|C0C1|1.0000 u
|C0C2|1.0000 u
|C0C3|1.0000 u
|C0C4|1.0000 u
|C0C5|1.0000 u
|C0C6|1.0000 u
|C0C8|0.2500 u
|C1C2|1.0000 u
|C1C3|1.7321 u
|C1C4|2.0000 u
|C1C5|1.7321 u
|C1C6|1.0000 u
|C1C7|1.0000 u
|C1C8|0.7500 u
|C2C3|1.0000 u
|C2C4|1.7321 u
|C2C5|2.0000 u
|C2C6|1.7321 u
|C2C7|1.0000 u
|C2C8|0.9014 u
|C3C4|1.0000 u
|C3C5|1.7321 u
|C3C6|2.0000 u
|C3C7|1.0000 u
|C3C8|1.1456 u
|C4C5|1.0000 u
|C4C6|1.7321 u
|C4C7|1.0000 u
|C4C8|1.2500 u
|C5C6|1.0000 u
|C5C7|1.0000 u
|C5C8|1.1456 u
|C6C7|1.0000 u
|C6C8|0.9014 u
|C7C8|0.2500 u

Derived ratios

|C0C8|1.000000
r(C1)2.000000
|C1C8|3.000000
|C2C8|3.605551
|C4C5|4.000000
|C3C8|4.582576
|C4C8|5.000000
|C1C3|6.928203
|C1C4|8.000000
f_i = f_0 × r_i · v1.0.0 · user-configured

Frequency derivation — centre distances

idr = d / Rexact (reference)sourcesf = f₀ × r
R10.2500000001/4|P0P7|220 × 1/4 = 55.000 Hz
R20.7500000003/4|P1P7|220 × 3/4 = 165.000 Hz
R30.901387819√13/4|P2P7| |P6P7|220 × √13/4 = 198.305 Hz
R41.0000000001|P0P1| |P0P2| |P0P3| …220 × 1 = 220.000 Hz
R51.145643924—|P3P7| |P5P7|220 × 1.145644 = 252.042 Hz
R61.2500000005/4|P4P7|220 × 5/4 = 275.000 Hz
R71.732050808√3|P1P3| |P1P5| |P2P4| …220 × √3 = 381.051 Hz
R82.0000000002|P1P4| |P2P5| |P3P6|220 × 2 = 440.000 Hz

Click a row to highlight its source points in the drawing. R = 1.0000 u. Exact forms are recognised reference values; the calculation itself is numeric. This mapping is a chosen design rule, not a law of nature.

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