Polygonal · 2D · v1.0.0
Regular n-gon
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Mathematics
Geometric construction
Regular polygon with a configurable number of sides n inscribed in a circle of radius R.
Symmetry: Dihedral Dn.
Culture
Symbolic interpretation
Configurable construction; no specific tradition implied.
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 | -0.6428 | 0.7660 | 0.0000 |
| P3 | -0.9848 | 0.1736 | 0.0000 |
| P4 | -0.8660 | -0.5000 | 0.0000 |
| P5 | -0.3420 | -0.9397 | 0.0000 |
| P6 | 0.3420 | -0.9397 | 0.0000 |
| P7 | 0.8660 | -0.5000 | 0.0000 |
| P8 | 0.9848 | 0.1736 | 0.0000 |
| P9 | 0.6428 | 0.7660 | 0.0000 |
Distances & angles
|P1P2|0.6840 u
|P2P3|0.6840 u
|P3P4|0.6840 u
|P4P5|0.6840 u
|P5P6|0.6840 u
|P6P7|0.6840 u
|P7P8|0.6840 u
|P8P9|0.6840 u
|P9P1|0.6840 u
r(C0)1.0000 u
∠P2P1P92.4435 rad
∠P1P2P32.4435 rad
∠P2P3P42.4435 rad
∠P3P4P52.4435 rad
∠P4P5P62.4435 rad
∠P5P6P72.4435 rad
∠P6P7P82.4435 rad
∠P7P8P92.4435 rad
∠P8P9P12.4435 rad
Derived ratios
|P5P6|1.000000
∠P2P1P91.000000
r(C0)1.461902
My Archive
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