A Hyperbolic Variant of Tic-Tac-Toe

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https://archive.bridgesmathart.org/2023/bridges2023-497.html

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http://hdl.handle.net/11603/28853

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection
UMBC Honors College
UMBC Psychology Department
UMBC Student Collection

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Date

2023

Type of Work

conference papers and proceedings
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Citation of Original Publication

Chen, Sarah, and Manil Suri. “A Hyperbolic Variant of Tic-Tac-Toe,” Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture (2023): 497–500. https://archive.bridgesmathart.org/2023/bridges2023-497.html.

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Subjects

tic-tac-toe on a truncated hyperbolic plane
tic-tac-toe on a sphere
variations of tic-tac-toe

Abstract

We consider a variation of tic-tac-toe played on a truncated hyperbolic plane, the inspiration for which arises from using crochet to create hyperbolic geometry. Instead of a 3×3 grid, we now have 13 cells. We show that using some modified rules, each player can again force a draw, as is the case for the usual flat version. We briefly consider tic-tac-toe on a sphere as well, for which we show that the same outcome of a draw holds. Finally, we present a strategy that can be used to choose the best move. Our game variations can be used pedagogically to engender more familiarity with non-Euclidean geometry.