Abstract
This Independent Study examines aperiodic tilings of the Euclidean plane, with particular attention to the recent discovery of an aperiodic monotile, or “einstein” tile. The project explores the mathematical foundations and historical development of tiling theory, establishing a framework for understanding how shapes can cover the plane without gaps or overlaps. Beginning with classical tiling theory and symmetry constraints on periodic patterns, the study develops the necessary background to distinguish periodic from aperiodic structures.
Building on this foundation, the paper analyzes major milestones in the study of aperiodicity, including Wang tiles, Penrose tiles, and Taylor–Socolar tiles, situating them within the broader search for a single shape capable of enforcing nonperiodicity without complex matching rules. By tracing the evolution of this problem and examining the mathematical ideas that led to the discovery of the einstein tile, this study highlights how questions of symmetry, infinity, and structure intersect in modern tiling theory.
Advisor
Pierce, Pamela
Department
Mathematics
Recommended Citation
Chasney, Brenna, "Tiling the Plane, Breaking the Rules: Aperiodicity and Infinity in Tiling Theory" (2026). Senior Independent Study Theses. Paper 13297.
https://openworks.wooster.edu/independentstudy/13297
Disciplines
Geometry and Topology | Other Mathematics
Keywords
Aperiodicity, Tiling Theory, Infinity, Aperiodic Monotile
Publication Date
2026
Degree Granted
Bachelor of Arts
Document Type
Senior Independent Study Thesis
© Copyright 2026 Brenna Chasney