Tessellations

In puzzles and recreational mathematics

Tessellations have given rise to many types of tiling puzzle, from traditional jigsaw puzzles (with irregular pieces of wood or cardboard) and the tangram, to more modern puzzles that often have a mathematical basis. For example, polyiamonds and polyominoes are figures of regular triangles and squares, often used in tiling puzzles. Authors such as Henry Dudeney and Martin Gardner have made many uses of tessellation in recreational mathematics. For example, Dudeney invented the hinged dissection, while Gardner wrote about the "rep-tile", a shape that can be dissected into smaller copies of the same shape. Inspired by Gardner's articles in Scientific American, the amateur mathematician Marjorie Rice found four new tessellations with pentagons. Squaring the square is the problem of tiling an integral square (one whose sides have integer length) using only other integral squares. An extension is squaring the plane, tiling it by squares whose sizes are all natural numbers without repetitions; James and Frederick Henle proved that this was possible.