Many people think that math and artists don't mix. That's just not true. M.C. Escher was a Dutch graphic artist who made mathematically-inspired woodcuts, lithographs, and mezzotints. Escher used math in his work with tessellations and the outcome was spectacular.
A tessellation is a tiling of geometric shapes on a flat surface. The shapes, or tiles, have no overlaps or gaps. Physical tessellations can be made of ceramic squares or hexagons. Tiling may be decorative, but often has a practical purpose like floor or wall coverings. Mosaic tilings often have geometric patterns. Some of the most celebrated tiling work in the world are the Moorish wall tilings of Islamic architecture.
Escher was inspired by the Moorish tilings when he visited Spain in 1936 and was struck by their use of symmetry. He wanted to create tessellations of recognizable figures—such as images of animals, people, and other everyday objects to which his viewers would relate. In his native tongue, tessellations are called 'Regelmatige Vlakverdeling', and he filled sketch books with drawings as he perfected his technique. Hyperbolic geometry is used in Escher's four “Circle Limit” woodcuts, one of which is pictured below. Escher created his tessellations by using fairly simple polygonal tessellations, which he then modified using isometries. Appearing as a pattern, his wood cuts use rotational symmetry at the center of its shapes.
Tessellations are an excellent example of math being used in art. While Escher is often the first artist people think of when they discuss art geometry, there are many other artists who have created notable work including Da Vinci and origami artist Robert Lang. So if you agree with the student in the comic at the beginning of the article and you lament the way artists use bleach, the next time you see a tessellation you may have a new appreciation for them.
MORE INFORMATION:
Tessellations by Recognizable Figures