Spirals · 2D · v1.0.0
Archimedean Spiral
Scroll to zoom, drag to pan, double-click to reset.
Mathematics
Geometric construction
r(θ) = a·θ with a = R / (2π·turns). Measurement points sampled at every quarter turn θ = kπ/2.
Symmetry: None (constant spacing between turns).
Culture
Symbolic interpretation
Seen in coiled ritual and natural forms; no fixed symbolic meaning.
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 | 0.0833 | 0.0000 |
| P2 | -0.1667 | 0.0000 | 0.0000 |
| P3 | -0.0000 | -0.2500 | 0.0000 |
| P4 | 0.3333 | -0.0000 | 0.0000 |
| P5 | 0.0000 | 0.4167 | 0.0000 |
| P6 | -0.5000 | 0.0000 | 0.0000 |
| P7 | -0.0000 | -0.5833 | 0.0000 |
| P8 | 0.6667 | -0.0000 | 0.0000 |
| P9 | 0.0000 | 0.7500 | 0.0000 |
| P10 | -0.8333 | 0.0000 | 0.0000 |
| P11 | -0.0000 | -0.9167 | 0.0000 |
| P12 | 1.0000 | -0.0000 | 0.0000 |
Distances & angles
|P1P2|0.1863 u
|P2P3|0.3005 u
|P3P4|0.4167 u
|P4P5|0.5336 u
|P5P6|0.6509 u
|P6P7|0.7683 u
|P7P8|0.8858 u
|P8P9|1.0035 u
|P9P10|1.1211 u
|P10P11|1.2388 u
|P11P12|1.3566 u
∠P1P2P31.4464 rad
∠P2P3P41.5153 rad
∠P3P4P51.5396 rad
∠P4P5P61.5508 rad
∠P5P6P71.5569 rad
∠P6P7P81.5606 rad
∠P7P8P91.5630 rad
∠P8P9P101.5646 rad
∠P9P10P111.5658 rad
∠P10P11P121.5667 rad
Derived ratios
|P1P2|1.000000
∠P1P2P31.000000
∠P2P3P41.047604
∠P3P4P51.064375
∠P4P5P61.072148
∠P5P6P71.076372
∠P6P7P81.078919
∠P7P8P91.080572
∠P8P9P101.081706
∠P9P10P111.082516
∠P10P11P121.083116
|P2P3|1.612452
|P3P4|2.236068
|P4P5|2.863564
|P5P6|3.492850
|P6P7|4.123106
|P7P8|4.753946
|P8P9|5.385165
|P9P10|6.016644
|P10P11|6.648308
|P11P12|7.280110
My Archive
Saved generations from this symbol
Nothing saved yet for Archimedean Spiral.