Dissections and Tilings

Recreations around geometric dissections (or dissections) are found in all civilizations. Squares, rectangles, polygons and, for about fifty years, polyominoes, provide an inexhaustible mine of puzzles whose elegance often lies in their simplicity. This area of geometry also holds real mathematical questions: can two figures of the same area be obtained, one from the other, using a simple pair of scissors? A theorem answers the question.

Regular tilings and friezes are now rigorously catalogued, but their diversity far exceeds initial intuition. In the 20th century, group theory indeed put an end to their apparent variety, thanks to the introduction of notations both clever and powerful. The subject seemed barely closed when non-regular tilings were discovered! Mathematician Roger Penrose and engraver Maurits Cornelis Escher were the precursors of these astonishing and magnificent new mosaics... whose riches Muslim artists had already glimpsed!