Step 2 of 4
Explore the Structure
Look at the construction, its points and its distances. Ratios between distances are what become frequencies.
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Geometry structure
The complete construction, whatever is shown in the drawing.
6
Points
shown
1
Circles
shown
5
Lines
shown
Measurements & ratios 3
Each length divided by the reference length gives a ratio r. These ratios become frequencies in the next step.
| Measurement | Length | Ratio r |
|---|---|---|
| |P4P5| | 1.1756 | 1.0000 |
| ∠P2P1P5 | 1.8850 | 1.0000 |
| |P1P4| | 1.9021 | 1.6180 |
Mathematical details
Regular 5-gon inscribed in a circle of radius R; vertex k at angle 90° + 360°·k/5. Side length = 2R·sin(π/5).
Symmetry: Dihedral D5.
Symbolic interpretation
The pentagon's diagonals stand in the golden ratio to its sides — a mathematical fact; its symbolic readings are cultural.