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Chakra · 2D · v1.0.0

Third Eye — Ajna

P0P1P2P3P4P5

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Mathematics

Geometric construction

Central circle of radius R; two petal circles of radius R/2 centred at (±1.5R, 0) so each touches the central circle; a downward equilateral triangle inscribed in the central circle.

Symmetry: Mirror symmetry about the vertical axis.

Culture

Symbolic interpretation

Two-petalled lotus with a downward triangle, associated with insight and intuition. 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
P11.50000.00000.0000
P2-1.50000.00000.0000
P3-0.0000-1.00000.0000
P40.86600.50000.0000
P5-0.86600.50000.0000

Distances & angles

|P3P4|1.7321 u
|P4P5|1.7321 u
|P5P3|1.7321 u
r(C0)1.0000 u
r(C1)0.5000 u
r(C2)0.5000 u
|C0C1|1.5000 u
|C0C2|1.5000 u
|C1C2|3.0000 u
∠P4P3P51.0472 rad
∠P3P4P51.0472 rad
∠P4P5P31.0472 rad

Derived ratios

r(C1)1.000000
∠P3P4P51.000000
r(C0)2.000000
|C0C1|3.000000
|P3P4|3.464102
|C1C2|6.000000
f_i = f_0 × r_i · v1.0.0 · user-configured

Frequency derivation — centre distances

idr = d / Rexact (reference)sourcesf = f₀ × r
R11.5000000003/2|P0P1| |P0P2|220 × 3/2 = 330.000 Hz
R23.0000000003|P1P2|220 × 3 = 660.000 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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