Chakra · 2D · v1.0.0

Heart Chakra — Anahata

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Mathematics

Geometric construction

Central circle of radius R; 12 touching petal circles of radius R·sin(π/12) centred on it; a hexagram of two equilateral triangles (point up and point down) inscribed in the central circle.

Symmetry: Dihedral D6 (petals alone are D12).

Culture

Symbolic interpretation

Twelve-petalled lotus with the six-pointed star, associated with air, love and balance. 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

id	x	y
P0	0.0000	0.0000
P1	0.0000	1.0000
P2	-0.5000	0.8660
P3	-0.8660	0.5000
P4	-1.0000	0.0000
P5	-0.8660	-0.5000
P6	-0.5000	-0.8660
P7	-0.0000	-1.0000
P8	0.5000	-0.8660
P9	0.8660	-0.5000
P10	1.0000	-0.0000
P11	0.8660	0.5000
P12	0.5000	0.8660

Distances & angles

|P1P5|1.7321 u

|P5P9|1.7321 u

|P9P1|1.7321 u

|P7P11|1.7321 u

|P11P3|1.7321 u

|P3P7|1.7321 u

r(C0)1.0000 u

r(C1)0.2588 u

r(C2)0.2588 u

r(C3)0.2588 u

r(C4)0.2588 u

r(C5)0.2588 u

r(C6)0.2588 u

r(C7)0.2588 u

r(C8)0.2588 u

r(C9)0.2588 u

r(C10)0.2588 u

r(C11)0.2588 u

r(C12)0.2588 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

|C0C7|1.0000 u

|C0C8|1.0000 u

|C0C9|1.0000 u

|C0C10|1.0000 u

|C0C11|1.0000 u

|C0C12|1.0000 u

|C1C2|0.5176 u

|C1C3|1.0000 u

|C1C4|1.4142 u

|C1C5|1.7321 u

|C1C6|1.9319 u

|C1C7|2.0000 u

|C1C8|1.9319 u

|C1C9|1.7321 u

|C1C10|1.4142 u

|C1C11|1.0000 u

|C1C12|0.5176 u

|C2C3|0.5176 u

|C2C4|1.0000 u

|C2C5|1.4142 u

|C2C6|1.7321 u

|C2C7|1.9319 u

|C2C8|2.0000 u

|C2C9|1.9319 u

|C2C10|1.7321 u

|C2C11|1.4142 u

|C2C12|1.0000 u

|C3C4|0.5176 u

|C3C5|1.0000 u

|C3C6|1.4142 u

|C3C7|1.7321 u

|C3C8|1.9319 u

|C3C9|2.0000 u

|C3C10|1.9319 u

|C3C11|1.7321 u

|C3C12|1.4142 u

|C4C5|0.5176 u

|C4C6|1.0000 u

|C4C7|1.4142 u

|C4C8|1.7321 u

|C4C9|1.9319 u

|C4C10|2.0000 u

|C4C11|1.9319 u

|C4C12|1.7321 u

|C5C6|0.5176 u

|C5C7|1.0000 u

|C5C8|1.4142 u

|C5C9|1.7321 u

|C5C10|1.9319 u

|C5C11|2.0000 u

|C5C12|1.9319 u

|C6C7|0.5176 u

|C6C8|1.0000 u

|C6C9|1.4142 u

|C6C10|1.7321 u

|C6C11|1.9319 u

|C6C12|2.0000 u

|C7C8|0.5176 u

|C7C9|1.0000 u

|C7C10|1.4142 u

|C7C11|1.7321 u

|C7C12|1.9319 u

|C8C9|0.5176 u

|C8C10|1.0000 u

|C8C11|1.4142 u

|C8C12|1.7321 u

|C9C10|0.5176 u

|C9C11|1.0000 u

|C9C12|1.4142 u

|C10C11|0.5176 u

|C10C12|1.0000 u

|C11C12|0.5176 u

∠P5P1P91.0472 rad

∠P1P5P91.0472 rad

∠P5P9P11.0472 rad

∠P11P7P31.0472 rad

∠P7P11P31.0472 rad

∠P11P3P71.0472 rad

Derived ratios

r(C1)1.000000

∠P11P7P31.000000

|C6C7|2.000000

|C6C8|3.863703

|C6C9|5.464102

|C4C8|6.692130

|C3C8|7.464102

|C2C8|7.727407

f_i = f_0 × r_i · v1.0.0 · user-configured

Frequency derivation — centre distances

Reference frequency f₀ (Hz)

id	r = d / R	exact (reference)	sources	f = f₀ × r
R1	0.517638090	—	\|P1P2\| \|P1P12\| \|P2P3\| …	220 × 0.517638 = 113.880 Hz
R2	1.000000000	1	\|P0P1\| \|P0P2\| \|P0P3\| …	220 × 1 = 220.000 Hz
R3	1.414213562	√2	\|P1P4\| \|P1P10\| \|P2P5\| …	220 × √2 = 311.127 Hz
R4	1.732050808	√3	\|P1P5\| \|P1P9\| \|P2P6\| …	220 × √3 = 381.051 Hz
R5	1.931851653	—	\|P1P6\| \|P1P8\| \|P2P7\| …	220 × 1.931852 = 425.007 Hz
R6	2.000000000	2	\|P1P7\| \|P2P8\| \|P3P9\| …	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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