Polygonal · 2D · v1.0.0
Square and Circle
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Mathematics
Geometric construction
A square of side 2R centred at the origin with its inscribed circle (radius R) and circumscribed circle (radius R√2).
Symmetry: Dihedral D4.
Culture
Symbolic interpretation
Associated in many traditions with the meeting of earth (square) and heaven (circle).
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 | 1.0000 | 1.0000 | 0.0000 |
| P2 | -1.0000 | 1.0000 | 0.0000 |
| P3 | -1.0000 | -1.0000 | 0.0000 |
| P4 | 1.0000 | -1.0000 | 0.0000 |
Distances & angles
|P1P2|2.0000 u
|P2P3|2.0000 u
|P3P4|2.0000 u
|P4P1|2.0000 u
r(C0)1.0000 u
r(C1)1.4142 u
∠P2P1P41.5708 rad
∠P1P2P31.5708 rad
∠P2P3P41.5708 rad
∠P3P4P11.5708 rad
Derived ratios
r(C0)1.000000
∠P2P1P41.000000
r(C1)1.414214
|P1P2|2.000000
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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