Root Chakra — Muladhara
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Geometric construction
Central circle of radius R; 4 petal circles of radius R·sin(π/4) centred on it at 90° steps; a square and a downward equilateral triangle inscribed in the central circle.
Symmetry: Dihedral D4 (petals and square); the triangle reduces the whole figure to a mirror symmetry.
Symbolic interpretation
Four-petalled lotus with square and downward triangle, associated with grounding and stability. Experimental chakra-inspired construction defined in this product; traditional chakra iconography varies and this is one reproducible reading of it.
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
Coordinates
| id | x | y | z |
|---|---|---|---|
| P0 | 0.0000 | 0.0000 | 0.0000 |
| P1 | 0.0000 | 1.0000 | 0.0000 |
| P2 | -1.0000 | 0.0000 | 0.0000 |
| P3 | -0.0000 | -1.0000 | 0.0000 |
| P4 | 1.0000 | -0.0000 | 0.0000 |
| P5 | -0.7071 | 0.7071 | 0.0000 |
| P6 | -0.7071 | -0.7071 | 0.0000 |
| P7 | 0.7071 | -0.7071 | 0.0000 |
| P8 | 0.7071 | 0.7071 | 0.0000 |
| P9 | 0.8660 | 0.5000 | 0.0000 |
| P10 | -0.8660 | 0.5000 | 0.0000 |
Distances & angles
Derived ratios
Frequency derivation — centre distances
| id | r = d / R | exact (reference) | sources | f = f₀ × r |
|---|---|---|---|---|
| R1 | 1.000000000 | 1 | |P0P1| |P0P2| |P0P3| … | 220 × 1 = 220.000 Hz |
| R2 | 1.414213562 | √2 | |P1P2| |P1P4| |P2P3| … | 220 × √2 = 311.127 Hz |
| R3 | 2.000000000 | 2 | |P1P3| |P2P4| | 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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