Escher's Mathematical Masterpieces

Ryan Mullee

His Life

Maurits C. Escher was born in 1898 in Leeuwarden, Holland. He was a printmaker, draftsman, book illustrator, tapestry designer, and muralist. He is most famous for his tessalation art. While attending the School of Architecture and Decorative Arts M.C. became interested in drawing and printmaking. In 1924 he married Jetta Umiker and spent years traveling through Europe drawing landscapes. In 1933 his interest in tessalations began. He traveled to Spain and viewed the tile patterns used in the Alhambra. After his visit there M.C. became obsessed with tessalations. He died in 1972 in a home for old artists.
The following are examples of his tessalations. To be a tessalation the objects must cover the whole plane with no overlaps or gaps.
Lions 1 - Eschers first tessalation.
Escher's Lizard tessailation used rotations.
Penrose Ghost was Escher's last tessalation. It was a solution to a puzzle.

Transformations

Escher utilized mathematical ideas in his tessalations. These are known as transformations. There are three main transformations. Rotation - turning an object around. Every rotation has a center and an angle. Translation - to move an object without rotating or reflecting it. Every translation has a direction and a distance. Reflection - to produce a mirror image of an object. Every reflection has a mirror line. Using these transformations he was able to cover the entire plane with no gaps or overlaps.