Circle-based · 2D · v1.0.0
Vesica Piscis
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Mathematics
Geometric construction
Two circles of radius R whose centres lie on each other's circumference (centre distance R). Intersections at (0, ±R√3/2).
Symmetry: Dihedral D2.
Culture
Symbolic interpretation
Used in medieval architecture and Christian iconography; associated with creation and the meeting of two worlds.
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 | -0.5000 | 0.0000 | 0.0000 |
| P1 | 0.5000 | 0.0000 | 0.0000 |
| P2 | 0.0000 | 0.8660 | 0.0000 |
| P3 | 0.0000 | -0.8660 | 0.0000 |
Distances & angles
|P0P1|1.0000 u
|P2P3|1.7321 u
|P0P2|1.0000 u
|P0P3|1.0000 u
|P1P2|1.0000 u
|P1P3|1.0000 u
r(C0)1.0000 u
r(C1)1.0000 u
|C0C1|1.0000 u
∠P1P0P21.0472 rad
∠P1P0P31.0472 rad
∠P2P0P32.0944 rad
∠P0P1P21.0472 rad
∠P0P1P31.0472 rad
∠P2P1P32.0944 rad
∠P3P2P00.5236 rad
∠P3P2P10.5236 rad
∠P0P2P11.0472 rad
∠P2P3P00.5236 rad
∠P2P3P10.5236 rad
∠P0P3P11.0472 rad
Derived ratios
|P0P2|1.000000
∠P3P2P01.000000
|P2P3|1.732051
∠P1P0P22.000000
∠P2P0P34.000000
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 |
|---|---|---|---|---|
| R1 | 1.000000000 | 1 | |P0P1| | 220 × 1 = 220.000 Hz |
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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