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Shrinkage Points of Golden Rectangle, Fibonacci Spirals, and Golden Spirals
- Source :
- Discrete Dynamics in Nature and Society, Vol 2019 (2019)
- Publication Year :
- 2019
- Publisher :
- Hindawi, 2019.
-
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.
- Subjects :
- Physics
0303 health sciences
Fibonacci number
Article Subject
lcsh:Mathematics
030303 biophysics
Mathematics::History and Overview
Geometry
Astrophysics::Cosmology and Extragalactic Astrophysics
lcsh:QA1-939
Curvature
03 medical and health sciences
Modeling and Simulation
Golden spiral
Golden rectangle
Polar
Polar coordinate system
Constant (mathematics)
Astrophysics::Galaxy Astrophysics
030304 developmental biology
Shrinkage
Subjects
Details
- Language :
- English
- ISSN :
- 10260226
- Database :
- OpenAIRE
- Journal :
- Discrete Dynamics in Nature and Society
- Accession number :
- edsair.doi.dedup.....0cd3587250485dffc6cb51f1480034b2
- Full Text :
- https://doi.org/10.1155/2019/3149602