A “Circle Limit III” Calculation

Year: 2007 Authors: Douglas Dunham

Core claim

For any (p,q,r) pattern, the intersection angle ω between the bounding circle and a backbone equidistant curve can be calculated, generalizing earlier results for special cases.

Topics

Circle Limit III, hyperbolic geometry, equidistant curves, pattern families, mathematical art

Domains

hyperbolic geometry, Poincaré disk model, Weierstrass model, geometry of curves, trigonometric calculation, M.C. Escher, tessellation, mathematical art

Methods

geometric derivation, model comparison, parameterized family analysis, pattern transformation, visual computation

Media

computer renditions, paper figures, hyperbolic disk model diagrams

Source status

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