Ptolemy, the Regular Heptagon, and Quasiperiodic Tilings

Year: 2022 Authors: Peter Stampfli; Theo P. Schaad

Core claim

Heptagon diagonal relations form a ring that determines valid inflation ratios and substitution patterns for seven-fold quasiperiodic rhombus tilings.

Topics

quasiperiodic tilings, regular heptagon geometry, inflation substitution, seven-fold symmetry

Domains

Euclidean geometry, Ptolemy’s theorem, algebraic number relations, tiling theory, geometric pattern design, mathematical visualization, decorative tilings

Methods

substitution method, cyclic quadrilateral analysis, geometric derivation, tiling construction

Media

rhombi, regular heptagon, browser-generated images

Source status

This page publishes metadata and extracted analytical signals only. Raw PDF and full OCR text are kept local for now.