A Topological Measure of Escher

[Images: Dream (early woodcut, 1935), Stars (polyhedron wood engraving, 1948), Vlinders aka Butterflies, (wood engraving, 1950), Circle Limit III (woodcut, 1959)].

Dutch graphic artist Maurits Cornelis (M.C.) Escher aka “ Mauk” was born June 17, 1898, in Leeuwarden, The Netherlands. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints.

  • He was a sickly child, and not very scholastic but excelled at drawing and carpentry, later studying decorative arts at the Haarlem School of Architecture and Decorative Arts.
  • He traveled through Italy and Spain where he was impressed by the Alhambra, the 14th-Century Moorish castle in Granada; with its intricate and decorative designs based on mathematical formulae; with interlocking repetitive patterns sculpted into the stone walls and ceilings.
  • This became a powerful influence on Escher’s works.

In his graphic art, the left-handed Escher portrayed mathematical relationships among shapes, figures and space; with interlocking figures using black and white to enhance different dimensions. Many of Escher’s works employed repeated tilings called tessellations. Integrated into his prints were mirror images of cones, spheres, cubes, rings and spirals. In his later years he also sketched insects.

Escher’s artwork is especially well liked by mathematicians and scientists, who enjoy his use of polyhedra and geometric distortions. Although he did not have any formal mathematical training, Escher’s understanding of mathematics was largely visual and intuitive. Nevertheless, his work had a strong mathematical component and more than a few of the worlds he drew were built around impossible objects such as the Necker Cube and the Penrose Triangle. Other mathematical principles evidenced in his works include the superposition of a hyperbolic plane on a fixed two-dimensional plane; and the incorporation of three-dimensional objects such as spheres, columns and cubes into his works.

  • Escher moved to the Rosa Spier Huis in Laren in 1970, a retirement home for artists where he had his own studio. He died at the home on 27 March 1972, at age 73.
  • Discover further information in The Graphic Work of M.C. Escher [book].

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