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Shrinkage Points of Golden Rectangle, Fibonacci Spirals, and Golden Spirals

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  • Jun-Sheng Duan

Abstract

We investigated the golden rectangle and the related Fibonacci spiral and golden spiral. The coordinates of the shrinkage points of a golden rectangle were derived. Properties of shrinkage points were discussed. Based on these properties, we conduct a comparison study for the Fibonacci spiral and golden spiral. Their similarities and differences were looked into by examining their polar coordinate equations, polar radii, arm-radius angles, and curvatures. The golden spiral has constant arm-radius angle and continuous curvature, while the Fibonacci spiral has cyclic varying arm-radius angle and discontinuous curvature.

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  • Jun-Sheng Duan, 2019. "Shrinkage Points of Golden Rectangle, Fibonacci Spirals, and Golden Spirals," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-6, December.
    • Handle: RePEc:hin:jnddns:3149602
    DOI: 10.1155/2019/3149602
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