M. C. Escher
1898 - 1972

"I can't stop fooling around with our irrefutable certainties. It is, for example, a pleasure knowingly to mix up two- and three-dimensionalities…to make fun of gravity…Are you really sure that a floor can't also be a ceiling? Are you definitely convinced that you will be on a higher plane when you walk up a staircase? Is it a fact as far as you are concerned that half an egg isn't also half an empty shell?" - M. C. Escher

Maurits Cornelis Escher was born in 1898 in Leeuwarden, Holland. His family pushed him to become an architect, following in his father's footsteps, but poor grades at the academy kept him from this career. Instead he decided to pursue his interest in graphic design. His artistic interpretations of the universe came in the forms of his specializations in woodcarving and lithographs. He is most recognized for his repeating geographic patterns (tessellations), his work with Platonic solids, representations of hyperbolic space, Topology, and special illusions.

When you first glance at Escher's work you see fascinating buildings, fish transforming into birds, reptiles coming in and out of books, and floors becoming ceilings and ceilings becoming floors. His work has intrigued mathematicians for many years. One of the questions being posed is how can he understand such concepts as division of the plane with no formal mathematics background? As Escher said himself, "By keenly confronting the enigmas that surround us, and by analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely innocent of training and knowledge in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists."

Escher drew his inspirations from mathematical ideas he read about. With this knowledge came the understanding of non-Euclidean geometry. Through this understanding he focused on the geometry of space and the logic of space. His interest in tessellations (arrangements of closed shapes that completely cover the plane without overlapping and without leaving gaps) led to his series named "Metamorphosis". He was able to distort animals, birds, and other figures to allow them to come in and out of the tessellation patterns.

Another area of interest was in Platonic solids, polyhedras with exactly similar polygonal faces. Examples of this are tetrahedrons with four triangular faces or the cube with six square faces. He represents this concept in "Order and Chaos" and "Stars".

Hyperbolic space and the idea of infinity can be seen in his woodcut "Circle Limit III" and "Snakes". Escher once expressed his view of infinity as follows:

"…It can apparently happen that someone, without much exact learning and with little of the information collected by earlier generations in his head, that such an individual, passing his days like other artists in the creation of more or less fantastic pictures, can one day feel ripen in himself a conscious wish to use his imaginary images to approach infinity as purely and as closely as possible."

The visual aspect of Topology interested Escher. Topology deals with properties of space, which are unchanged by distortions which may stretch or bend it, but which do not tear or puncture it. The "Mobius Strip" is a good example of the bending of space. If you follow the path of the ants you will observe that they are walking on one side of the strip. Escher has also created closed water systems for us to ponder as in "Waterfall". Where is the water coming from and which direction is it flowing?

"I try in my prints to testify that we live in a beautiful and orderly world, not in a chaos without norms, even though that is how it sometimes appears. My subjects are also often playful. I cannot refrain from demonstrating the nonsensicalness of some of what we take to be irrefutable certainties. It is, for example, a pleasure to deliberately mix together objects of two and three dimensions, surface and spatial relationships, and to make fun of gravity."
From 1922 till his death in 1972 Escher astounded mathematicians and artists with his artistic ability and knowledge of space. He was able to tie the realms of mathematics and art into beautiful works of art and entertainment.

To view Escher's work connect to these websites:
http://www.worldofescher.com
http://www.mathacademy.com/patonic_realms/minitext/escher.html

Contributed by Carey Eskridge Lybarger

References:

  1. J. L. Locher. The World of M. C. Escher. Amsterdam: Menlenjoff International. 1971.
  2. http://www.worldofescher.com
  3. http://www.mathacademy.com/platonic_realms/minitext/escher.html
  4. http://www.iproject.com/escher/biography.html

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