Spirals · 2D · v1.0.0
Golden Spiral
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Mathematics
Geometric construction
Logarithmic spiral with growth factor φ per quarter turn: b = ln(φ)/(π/2). This is a documented approximation framework; the Fibonacci-square spiral approximates it.
Symmetry: Self-similar (ratio φ every 90°).
Culture
Symbolic interpretation
Widely linked to aesthetics and nature; many such claims are overstated.
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 | 0.0050 | 0.0000 |
| P2 | -0.0081 | 0.0000 | 0.0000 |
| P3 | -0.0000 | -0.0132 | 0.0000 |
| P4 | 0.0213 | -0.0000 | 0.0000 |
| P5 | 0.0000 | 0.0344 | 0.0000 |
| P6 | -0.0557 | 0.0000 | 0.0000 |
| P7 | -0.0000 | -0.0902 | 0.0000 |
| P8 | 0.1459 | -0.0000 | 0.0000 |
| P9 | 0.0000 | 0.2361 | 0.0000 |
| P10 | -0.3820 | 0.0000 | 0.0000 |
| P11 | -0.0000 | -0.6180 | 0.0000 |
| P12 | 1.0000 | -0.0000 | 0.0000 |
Distances & angles
|P1P2|0.0096 u
|P2P3|0.0155 u
|P3P4|0.0250 u
|P4P5|0.0405 u
|P5P6|0.0655 u
|P6P7|0.1060 u
|P7P8|0.1715 u
|P8P9|0.2775 u
|P9P10|0.4490 u
|P10P11|0.7265 u
|P11P12|1.1756 u
∠P1P2P31.5708 rad
∠P2P3P41.5708 rad
∠P3P4P51.5708 rad
∠P4P5P61.5708 rad
∠P5P6P71.5708 rad
∠P6P7P81.5708 rad
∠P7P8P91.5708 rad
∠P8P9P101.5708 rad
∠P9P10P111.5708 rad
∠P10P11P121.5708 rad
Derived ratios
|P1P2|1.000000
∠P10P11P121.000000
|P2P3|1.618034
|P3P4|2.618034
|P4P5|4.236068
|P5P6|6.854102
|P6P7|11.090170
|P7P8|17.944272
|P8P9|29.034442
|P9P10|46.978714
|P10P11|76.013156
|P11P12|122.991869
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