Radial · 2D · v1.0.0
Seven-Fold Radial
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Mathematics
Geometric construction
7 points on a circle of radius R joined as the star polygon {7/step}, with spokes to the centre and the star's inner circle.
Symmetry: Dihedral D7.
Culture
Symbolic interpretation
Seven-fold forms are linked to planets and weekdays in many cultures.
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 | -0.7818 | 0.6235 | 0.0000 |
| P3 | -0.9749 | -0.2225 | 0.0000 |
| P4 | -0.4339 | -0.9010 | 0.0000 |
| P5 | 0.4339 | -0.9010 | 0.0000 |
| P6 | 0.9749 | -0.2225 | 0.0000 |
| P7 | 0.7818 | 0.6235 | 0.0000 |
Distances & angles
|P1P4|1.9499 u
|P0P1|1.0000 u
|P2P5|1.9499 u
|P0P2|1.0000 u
|P3P6|1.9499 u
|P0P3|1.0000 u
|P4P7|1.9499 u
|P0P4|1.0000 u
|P5P1|1.9499 u
|P0P5|1.0000 u
|P6P2|1.9499 u
|P0P6|1.0000 u
|P7P3|1.9499 u
|P0P7|1.0000 u
r(C0)1.0000 u
r(C1)0.2225 u
∠P4P1P00.2244 rad
∠P4P1P50.4488 rad
∠P0P1P50.2244 rad
∠P1P4P70.4488 rad
∠P1P4P00.2244 rad
∠P7P4P00.2244 rad
∠P1P0P20.8976 rad
∠P1P0P31.7952 rad
∠P1P0P42.6928 rad
∠P1P0P52.6928 rad
∠P1P0P61.7952 rad
∠P1P0P70.8976 rad
∠P2P0P30.8976 rad
∠P2P0P41.7952 rad
∠P2P0P52.6928 rad
∠P2P0P62.6928 rad
∠P2P0P71.7952 rad
∠P3P0P40.8976 rad
∠P3P0P51.7952 rad
∠P3P0P62.6928 rad
∠P3P0P72.6928 rad
∠P4P0P50.8976 rad
∠P4P0P61.7952 rad
∠P4P0P72.6928 rad
∠P5P0P60.8976 rad
∠P5P0P71.7952 rad
∠P6P0P70.8976 rad
∠P5P2P00.2244 rad
∠P5P2P60.4488 rad
∠P0P2P60.2244 rad
∠P2P5P10.4488 rad
∠P2P5P00.2244 rad
∠P1P5P00.2244 rad
∠P6P3P00.2244 rad
∠P6P3P70.4488 rad
∠P0P3P70.2244 rad
∠P3P6P20.4488 rad
∠P3P6P00.2244 rad
∠P2P6P00.2244 rad
∠P4P7P30.4488 rad
∠P4P7P00.2244 rad
∠P3P7P00.2244 rad
Derived ratios
r(C1)1.000000
∠P0P1P51.000000
∠P5P2P62.000000
∠P2P0P34.000000
|P0P1|4.493959
∠P1P0P38.000000
|P1P4|8.762573
∠P1P0P412.000000
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 |
|---|
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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