A Hyperbolic Variant 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.