Art and Recreational Math Based on Kite-Tiling Rosettes
Robert Fathauer

Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture
Pages 15–22
Regular Papers

Abstract

We describe here some properties of kite-tiling rosettes and the wide range of artistic and recreational mathematics uses of kite-tiling rosettes. A kite-tiling rosette is a tiling with a single kite-shaped prototile and a singular point about which the tiling has rotational symmetry. A tiling with n-fold symmetry is comprised of rings of n kites of the same size, with kite size increasing with distance away from the singular point. The prototile can be either convex or concave. Such tilings can be constructed over a wide range of kite shapes for all n > 2, and for concave kites for n = 2. A finite patch of adjacent rings of tiles can serve as a scaffolding for constructing knots and links, with strands lying along tile edges. Such patches serve as convenient templates for attractive graphic designs and Escheresque artworks. In addition, these patches can be used as grids for a variety of puzzles and games and are particularly well suited to pandiagonal magic squares. Three-dimensional structures created by giving the tiles thickness are also explored.

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