Chakra · 2D · v1.0.0
Throat Chakra — Vishuddha
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Mathematics
Geometric construction
Central circle of radius R; 16 touching petal circles of radius R·sin(π/16) centred on it; a downward equilateral triangle inscribed in the central circle, with an inner circle of radius R/2 inside it (the triangle's incircle).
Symmetry: Mirror symmetry (petals alone are D16).
Culture
Symbolic interpretation
Sixteen-petalled lotus with triangle and full moon circle, associated with ether and expression. 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 | -0.3827 | 0.9239 | 0.0000 |
| P3 | -0.7071 | 0.7071 | 0.0000 |
| P4 | -0.9239 | 0.3827 | 0.0000 |
| P5 | -1.0000 | 0.0000 | 0.0000 |
| P6 | -0.9239 | -0.3827 | 0.0000 |
| P7 | -0.7071 | -0.7071 | 0.0000 |
| P8 | -0.3827 | -0.9239 | 0.0000 |
| P9 | -0.0000 | -1.0000 | 0.0000 |
| P10 | 0.3827 | -0.9239 | 0.0000 |
| P11 | 0.7071 | -0.7071 | 0.0000 |
| P12 | 0.9239 | -0.3827 | 0.0000 |
| P13 | 1.0000 | -0.0000 | 0.0000 |
| P14 | 0.9239 | 0.3827 | 0.0000 |
| P15 | 0.7071 | 0.7071 | 0.0000 |
| P16 | 0.3827 | 0.9239 | 0.0000 |
| P17 | 0.8660 | 0.5000 | 0.0000 |
| P18 | -0.8660 | 0.5000 | 0.0000 |
Distances & angles
|P9P17|1.7321 u
|P17P18|1.7321 u
|P18P9|1.7321 u
r(C0)1.0000 u
r(C1)0.1951 u
r(C2)0.1951 u
r(C3)0.1951 u
r(C4)0.1951 u
r(C5)0.1951 u
r(C6)0.1951 u
r(C7)0.1951 u
r(C8)0.1951 u
r(C9)0.1951 u
r(C10)0.1951 u
r(C11)0.1951 u
r(C12)0.1951 u
r(C13)0.1951 u
r(C14)0.1951 u
r(C15)0.1951 u
r(C16)0.1951 u
r(C17)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
|C0C7|1.0000 u
|C0C8|1.0000 u
|C0C9|1.0000 u
|C0C10|1.0000 u
|C0C11|1.0000 u
|C0C12|1.0000 u
|C0C13|1.0000 u
|C0C14|1.0000 u
|C0C15|1.0000 u
|C0C16|1.0000 u
|C1C2|0.3902 u
|C1C3|0.7654 u
|C1C4|1.1111 u
|C1C5|1.4142 u
|C1C6|1.6629 u
|C1C7|1.8478 u
|C1C8|1.9616 u
|C1C9|2.0000 u
|C1C10|1.9616 u
|C1C11|1.8478 u
|C1C12|1.6629 u
|C1C13|1.4142 u
|C1C14|1.1111 u
|C1C15|0.7654 u
|C1C16|0.3902 u
|C1C17|1.0000 u
|C2C3|0.3902 u
|C2C4|0.7654 u
|C2C5|1.1111 u
|C2C6|1.4142 u
|C2C7|1.6629 u
|C2C8|1.8478 u
|C2C9|1.9616 u
|C2C10|2.0000 u
|C2C11|1.9616 u
|C2C12|1.8478 u
|C2C13|1.6629 u
|C2C14|1.4142 u
|C2C15|1.1111 u
|C2C16|0.7654 u
|C2C17|1.0000 u
|C3C4|0.3902 u
|C3C5|0.7654 u
|C3C6|1.1111 u
|C3C7|1.4142 u
|C3C8|1.6629 u
|C3C9|1.8478 u
|C3C10|1.9616 u
|C3C11|2.0000 u
|C3C12|1.9616 u
|C3C13|1.8478 u
|C3C14|1.6629 u
|C3C15|1.4142 u
|C3C16|1.1111 u
|C3C17|1.0000 u
|C4C5|0.3902 u
|C4C6|0.7654 u
|C4C7|1.1111 u
|C4C8|1.4142 u
|C4C9|1.6629 u
|C4C10|1.8478 u
|C4C11|1.9616 u
|C4C12|2.0000 u
|C4C13|1.9616 u
|C4C14|1.8478 u
|C4C15|1.6629 u
|C4C16|1.4142 u
|C4C17|1.0000 u
|C5C6|0.3902 u
|C5C7|0.7654 u
|C5C8|1.1111 u
|C5C9|1.4142 u
|C5C10|1.6629 u
|C5C11|1.8478 u
|C5C12|1.9616 u
|C5C13|2.0000 u
|C5C14|1.9616 u
|C5C15|1.8478 u
|C5C16|1.6629 u
|C5C17|1.0000 u
|C6C7|0.3902 u
|C6C8|0.7654 u
|C6C9|1.1111 u
|C6C10|1.4142 u
|C6C11|1.6629 u
|C6C12|1.8478 u
|C6C13|1.9616 u
|C6C14|2.0000 u
|C6C15|1.9616 u
|C6C16|1.8478 u
|C6C17|1.0000 u
|C7C8|0.3902 u
|C7C9|0.7654 u
|C7C10|1.1111 u
|C7C11|1.4142 u
|C7C12|1.6629 u
|C7C13|1.8478 u
|C7C14|1.9616 u
|C7C15|2.0000 u
|C7C16|1.9616 u
|C7C17|1.0000 u
|C8C9|0.3902 u
|C8C10|0.7654 u
|C8C11|1.1111 u
|C8C12|1.4142 u
|C8C13|1.6629 u
|C8C14|1.8478 u
|C8C15|1.9616 u
|C8C16|2.0000 u
|C8C17|1.0000 u
|C9C10|0.3902 u
|C9C11|0.7654 u
|C9C12|1.1111 u
|C9C13|1.4142 u
|C9C14|1.6629 u
|C9C15|1.8478 u
|C9C16|1.9616 u
|C9C17|1.0000 u
|C10C11|0.3902 u
|C10C12|0.7654 u
|C10C13|1.1111 u
|C10C14|1.4142 u
|C10C15|1.6629 u
|C10C16|1.8478 u
|C10C17|1.0000 u
|C11C12|0.3902 u
|C11C13|0.7654 u
|C11C14|1.1111 u
|C11C15|1.4142 u
|C11C16|1.6629 u
|C11C17|1.0000 u
|C12C13|0.3902 u
|C12C14|0.7654 u
|C12C15|1.1111 u
|C12C16|1.4142 u
|C12C17|1.0000 u
|C13C14|0.3902 u
|C13C15|0.7654 u
|C13C16|1.1111 u
|C13C17|1.0000 u
|C14C15|0.3902 u
|C14C16|0.7654 u
|C14C17|1.0000 u
|C15C16|0.3902 u
|C15C17|1.0000 u
|C16C17|1.0000 u
∠P17P9P181.0472 rad
∠P9P17P181.0472 rad
∠P17P18P91.0472 rad
Derived ratios
r(C1)1.000000
∠P9P17P181.000000
|C10C11|2.000000
r(C17)2.562915
|C10C12|3.923141
r(C0)5.125831
|C5C8|5.695518
|C4C8|7.249020
|C3C8|8.523945
|P9P17|8.878200
|C10C16|9.471301
|C1C8|10.054679
|C1C9|10.251662
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 | 0.390180644 | — | |P1P2| |P1P16| |P2P3| … | 220 × 0.390181 = 85.840 Hz |
| R2 | 0.765366865 | — | |P1P3| |P1P15| |P2P4| … | 220 × 0.765367 = 168.381 Hz |
| R3 | 1.000000000 | 1 | |P0P1| |P0P2| |P0P3| … | 220 × 1 = 220.000 Hz |
| R4 | 1.111140466 | — | |P1P4| |P1P14| |P2P5| … | 220 × 1.111140 = 244.451 Hz |
| R5 | 1.414213562 | √2 | |P1P5| |P1P13| |P2P6| … | 220 × √2 = 311.127 Hz |
| R6 | 1.662939225 | — | |P1P6| |P1P12| |P2P7| … | 220 × 1.662939 = 365.847 Hz |
| R7 | 1.847759065 | — | |P1P7| |P1P11| |P2P8| … | 220 × 1.847759 = 406.507 Hz |
| R8 | 1.961570561 | — | |P1P8| |P1P10| |P2P9| … | 220 × 1.961571 = 431.546 Hz |
| R9 | 2.000000000 | 2 | |P1P9| |P2P10| |P3P11| … | 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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