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.
18
Points
shown
0
Circles
none in this shape
31
Lines
shown
Measurements & ratios 21
Each length divided by the reference length gives a ratio r. These ratios become frequencies in the next step.
| Measurement | Length | Ratio r |
|---|---|---|
| |P0P1| | 0.0588 | 1.0000 |
| |P6P0| | 0.1176 | 2.0000 |
| |P9P1| | 0.1765 | 3.0000 |
| ρ(P8) | 0.2775 | 4.7170 |
| |P9P10| | 0.2941 | 5.0000 |
| ρ(P9) | 0.4000 | 6.8007 |
| ρ(P6) | 0.4372 | 7.4330 |
| |P7P11| | 0.4706 | 8.0000 |
| ρ(P0) | 0.4895 | 8.3217 |
| ρ(P1) | 0.5237 | 8.9022 |
| ρ(P3) | 0.5399 | 9.1788 |
| ρ(P7) | 0.5495 | 9.3408 |
| ρ(P2) | 0.5711 | 9.7082 |
| ρ(P5) | 0.5919 | 10.0623 |
| ρ(P4) | 0.6204 | 10.5475 |
| ρ(P10) | 0.6609 | 11.2361 |
| |P8P13| | 0.7647 | 13.0000 |
| ρ(P11) | 0.8135 | 13.8293 |
| ρ(P13) | 1.0108 | 17.1828 |
| ρ(P12) | 1.1754 | 19.9812 |
| |P16P17| | 1.2353 | 21.0000 |
Mathematical details
Squares with side lengths F₁…Fₙ placed counter-clockwise (right, up, left, down); a quarter-circle arc of radius Fₖ is drawn in each square. Scaled to fit 2R.
Symmetry: None; approximates the golden spiral as n grows.
Symbolic interpretation
Popular emblem of 'nature's code'; a mathematical approximation.