Golden-Ratio-Based Rectangular Tilings

zbMATH Open1401.52029arXiv1611.01182MaRDI QIDQ4555773

Mark Bryant, D. W. Hobill

Publication date: 21 November 2018

Abstract: A golden-ratio-based rectangular tiling of the first quadrant of the Euclidean plane is constructed by drawing vertical and horizontal grid lines which are located at all even powers of $phi$ along one axis, and at all odd powers of $phi$ on the other axis. The vertices of the rectangles formed by these lines can be connected by rays starting at the origin having slopes that are odd powers of $phi$. A refinement of this tiling results in the familiar one with horizontal and vertical grid lines at every power of $phi$ along each axis. Geometric proofs of the convergence of several known power series' in $phi$ are provided.

Full work available at URL: https://arxiv.org/abs/1611.01182

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Tilings in (2) dimensions (aspects of discrete geometry) (52C20)

This page was built for publication: Golden-Ratio-Based Rectangular Tilings

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q4555773)