The Subtle Symmetry of Golden Spirals

Year: 2000 Authors: Alvin Swimmer

Core claim

Golden spirals arise from iterative Castor and golden-rectangle constructions whose Φ-map generates tangent-smooth spirals with a shared eye and harmonic line structure.

Topics

golden ratio geometry, iterative spiral construction, harmonic division, symmetry and transformation

Domains

Euclidean geometry, golden ratio, projective geometry, transformational geometry, mathematical art, visual pattern design, architecture

Methods

geometric construction, iterative mapping, ratio analysis, diagrammatic proof

Media

triangles, golden rectangles, spiral arcs, figures

Source status

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