Theodorus Tiles

A book of patterns created by dividing the equilateral triangle into a set of tangram-like shapes tiles.

This booklet explores some 180 patterns created from an interesting division of the equilateral triangle. The divisions include three idealised triangles and quadrilaterals. The equilateral (A), right-angled scalene (E), and isosceles (F) triangle appear alongside the parrellogram (B), trapezium (C) and square (D). The reappearance of the square root of three, or Theodorus constant, gives the tiles their name.

1+√3 1+√3 √3 1 1 1 √3 √3 √3 √3 √3 √3 1 2•√3 2 A B C E D F

Each pattern is made using one of three rotations of the tiles, and iterating through every combination as the tiles alternate between black and white.

Tile rotations

The arrangement of the tiles includes just enough complexity to create interesting patterns that often rhyme but never repeat each other. In fact, the variation in the patterns is surprising given the structured nature of the input.

Example patterns

An initial run of 25 limited edition booklets in A5 format was printed in 2022.

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