A geometric proof of the Affability Theorem for planar tilings
Fernando Alcalde Cuesta, Pablo Gonz\'alez Sequeiros, \'Alvaro Lozano, Rojo
TL;DR
This paper provides a geometric proof of the Affability Theorem for aperiodic, repetitive planar tilings, offering new insights into their structural properties.
Contribution
It introduces a geometric approach to proving the Affability Theorem, expanding understanding of planar tilings beyond previous algebraic methods.
Findings
Geometric proof of the Affability Theorem for planar tilings
Enhanced understanding of the structure of aperiodic, repetitive tilings
Potential applications in tiling classification and dynamical systems
Abstract
We give a geometric proof of the Affability Theorem of T. Giordano, H. Matui, I. Putnam and C. Skau for aperiodic and repetitive planar tilings.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Computational Geometry and Mesh Generation · Structural Analysis and Optimization