Chakra · 2D · v1.0.0
Solar Plexus — Manipura
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Mathematics
Geometric construction
Central circle of radius R; 10 touching petal circles of radius R·sin(π/10) centred on it; a downward equilateral triangle inscribed in the central circle.
Symmetry: Mirror symmetry (petals alone are D10).
Culture
Symbolic interpretation
Ten-petalled lotus with a downward triangle, associated with fire and personal will. 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 | z |
|---|---|---|---|
| P0 | 0.0000 | 0.0000 | 0.0000 |
| P1 | 0.0000 | 1.0000 | 0.0000 |
| P2 | -0.5878 | 0.8090 | 0.0000 |
| P3 | -0.9511 | 0.3090 | 0.0000 |
| P4 | -0.9511 | -0.3090 | 0.0000 |
| P5 | -0.5878 | -0.8090 | 0.0000 |
| P6 | -0.0000 | -1.0000 | 0.0000 |
| P7 | 0.5878 | -0.8090 | 0.0000 |
| P8 | 0.9511 | -0.3090 | 0.0000 |
| P9 | 0.9511 | 0.3090 | 0.0000 |
| P10 | 0.5878 | 0.8090 | 0.0000 |
| P11 | 0.8660 | 0.5000 | 0.0000 |
| P12 | -0.8660 | 0.5000 | 0.0000 |
Distances & angles
|P6P11|1.7321 u
|P11P12|1.7321 u
|P12P6|1.7321 u
r(C0)1.0000 u
r(C1)0.3090 u
r(C2)0.3090 u
r(C3)0.3090 u
r(C4)0.3090 u
r(C5)0.3090 u
r(C6)0.3090 u
r(C7)0.3090 u
r(C8)0.3090 u
r(C9)0.3090 u
r(C10)0.3090 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
|C1C2|0.6180 u
|C1C3|1.1756 u
|C1C4|1.6180 u
|C1C5|1.9021 u
|C1C6|2.0000 u
|C1C7|1.9021 u
|C1C8|1.6180 u
|C1C9|1.1756 u
|C1C10|0.6180 u
|C2C3|0.6180 u
|C2C4|1.1756 u
|C2C5|1.6180 u
|C2C6|1.9021 u
|C2C7|2.0000 u
|C2C8|1.9021 u
|C2C9|1.6180 u
|C2C10|1.1756 u
|C3C4|0.6180 u
|C3C5|1.1756 u
|C3C6|1.6180 u
|C3C7|1.9021 u
|C3C8|2.0000 u
|C3C9|1.9021 u
|C3C10|1.6180 u
|C4C5|0.6180 u
|C4C6|1.1756 u
|C4C7|1.6180 u
|C4C8|1.9021 u
|C4C9|2.0000 u
|C4C10|1.9021 u
|C5C6|0.6180 u
|C5C7|1.1756 u
|C5C8|1.6180 u
|C5C9|1.9021 u
|C5C10|2.0000 u
|C6C7|0.6180 u
|C6C8|1.1756 u
|C6C9|1.6180 u
|C6C10|1.9021 u
|C7C8|0.6180 u
|C7C9|1.1756 u
|C7C10|1.6180 u
|C8C9|0.6180 u
|C8C10|1.1756 u
|C9C10|0.6180 u
∠P11P6P121.0472 rad
∠P6P11P121.0472 rad
∠P11P12P61.0472 rad
Derived ratios
r(C1)1.000000
∠P6P11P121.000000
|C1C2|2.000000
r(C0)3.236068
|C2C4|3.804226
|C3C6|5.236068
|P6P11|5.605034
|C1C7|6.155367
|C1C6|6.472136
f_i = f_0 × r_i · v1.0.0 · user-configured
Frequency derivation — centre distances
| id | r = d / R | exact (reference) | sources | f = f₀ × r |
|---|---|---|---|---|
| R1 | 0.618033989 | φ^-1 | |P1P2| |P1P10| |P2P3| … | 220 × φ^-1 = 135.967 Hz |
| R2 | 1.000000000 | 1 | |P0P1| |P0P2| |P0P3| … | 220 × 1 = 220.000 Hz |
| R3 | 1.175570505 | — | |P1P3| |P1P9| |P2P4| … | 220 × 1.175571 = 258.626 Hz |
| R4 | 1.618033989 | φ | |P1P4| |P1P8| |P2P5| … | 220 × φ = 355.967 Hz |
| R5 | 1.902113033 | — | |P1P5| |P1P7| |P2P6| … | 220 × 1.902113 = 418.465 Hz |
| R6 | 2.000000000 | 2 | |P1P6| |P2P7| |P3P8| … | 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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