Scholarlink

We apply Ptolemy’s theorem to regular polygons, obtaining integer rings. They are essential for creating substitution rules for quasiperiodic tilings using rhombic tiles. We discuss this in detail for tilings of 5-, 8-, and 12-fold rotational symmetry. Fractals are hidden in these tilings. We make them visible by using image manipulation or special substitution rules.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Quasiperiodic Tilings from Ptolemy’s Theorem as Applied to Regular Polygons

  • 动态工具书词条

  • 发表日期：

    2025年

查看全文
  • Peter Stampfli,
  • Theo P. Schaad

摘要

We apply Ptolemy’s theorem to regular polygons, obtaining integer rings. They are essential for creating substitution rules for quasiperiodic tilings using rhombic tiles. We discuss this in detail for tilings of 5-, 8-, and 12-fold rotational symmetry. Fractals are hidden in these tilings. We make them visible by using image manipulation or special substitution rules.