An Orthogonal Mate for a Latin Square Based on an Asymmetric Tile, II
Stephen M. Gagola Jr.

Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture
Pages 123–130
Regular Papers

Abstract

We describe here the second of two asymmetric tiles created by the artist Peter Raedschelders in his construction of an 8 by 8 Latin square. The symbols of the square are the eight distinct orientations of the tile, and these fit snugly together in the style of M. C. Escher to form the Latin square. Unlike his first tile which uses even and odd functions to describe the sides of the tile, the artist’s second tile may be constructed from an arbitrary (but reasonable) curve appearing on one side of the tile, with the other sides being determined from this. By using some algebra and colors, we illustrate that the resulting Latin square has an orthogonal mate.

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