A Hyperbolic Variant of Tic-Tac-Toe
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2023
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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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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.