Escher.jpg Maurtis Cornelis's Escher

M.C. Escher was not a mathematician. In fact, he never had formal math training after high school. He was an artist. He made over 448 lithographs, wood cuts, and wood engravings, and over 2000 sketches and drawings. (Biography of M.C. Escher) You may ask yourself, "How is M.C. Escher relevant to this project if he was not a mathematician." This question will be answered through a short summery of his life and how it related to math and the geography of space and the logic of space.

Escher's Life

M.C. Escher's real name is Maurits Cornelis Escher. He was called Mauk for short. Escher was born on June 17th, 1898. He was the youngest of three boys and his older brothers' names were Arnold and Beer. Escher was born in Leeuwardin, Holland and lived there until he was five. When he was five, Escher and his family moved to Arnhem to improve his health.(M.C. Escher Brief Biography.) It was in Arnhem that Escher went to school through grade twelve. He took up piano and woodworking, but it was in drawing where he had the most skill. In fact, all of his grades were low in school, except for in drawing class. Though he was best at drawing, Escher did not know that he wanted to be an artist, not yet.
In school, Escher was not the best student at all. He failed his final exam and never officially graduated.(M.C. Escher Brief Biography) This was not a good thing for him because he was expected to become an architect by his family, especially his father, George Escher, who was a civil engineer. However, Escher started to get a little more interested in art in religion school in 1913, when he met his best friend, Bas Kist. Kist and Escher developed an interest in printing.
For the next eleven or so years, Escher traveled all around Europe to get inspiration for art and go to school. On June 12th, 1925, Escher married a woman names Jetta Umiker who was apart of a family that was living in the same building as Escher in Italy. The couple settled in Rome for eleven years. They had two children, George and Arthur. In the time that the couple was in Rome, Escher became very popular and had five exhibits in one year. However his health was beginning to become an issue again and his work and popularity were on hold. (M.C. Escher Brief Biography.)

How He Included Math

Beginning in the 1940's many mathematicians began to notice Escher's work. They appreciated his use of symmetry and impossible figures. (M.C. Escher Brief Biography.) They noticed that he used perspective and liked the idea of infinity. For example. in figure 1, Three Spheres,3194472469_155f51b512.jpg
Escher shows the three spheres that the artist in the picture is drawing. In the middle sphere, shows the reflection of the artist who is drawing the spheres. This shows some what of a cycle that loops back around/infinity.
pro3esc_a.jpg FIGURE 2
Similarly in figure two, Mobius Strip II, it looks as if the ants are walking on opposite sides of the strip, but if looked at closely, they are on the same side. To test this, a Mobius Strip can be made by cutting a strip of paper, making a small twist in it, and taping the two ends. (The Mathematical Art of M.C. Escher)

Escher also played around with TESSELLATIONS. A tessellation is a plane (for example a piece of paper) with a collage of the same type of shapes totally covering the plane, without any overlaps or gaps, like in FIGURE 3.
In FIGURE 3, the crocodile comes out of a tessellation of crocodile shapes and crawls over a series objects and back into the tessellation.
Escher_1.jpgFIGURE 3
Escher often used animals and weird creatures in his tessellations, and in other paintings too, like in FIGURE 4 and FIGURE 5.
escher03.jpgFIGURE 4 FIGURE 5
We don't really know why he used animals so much, or why he loved them, but it is clear that he did. He said, "While I was sitting so quietly alone, a very small bird hopped over the snow-perhaps it was a wren. It was enjoying the weather; it blinked merrily at the sun. It skipped toward the water and fluttered about a bit. Then it flew away, so I left too." This shows that he appreciated nature and took all of it in to include it in his art.

Many of Escher's works are shown as optical illusions. Some are in museums, and some are in kids' play places, like a Florida science hands-on museum, Wonder Works. Though Escher liked optical illusions, they were not the starting point of his work. (M.C. Escher Legacy: A Centennial Celebration. P. 7) FIGURE 6 shows a simple panting by Escher. It looks as though one box is longer than the other, but if measured, they are exactly the same. FIGURE 2 could also be considered an optical illusion.
Screen_shot_2010-02-23_at_10.28.46_AM.png FIGURE 6

Escher also loved impossible figures, and that is one of the things that the circle of mathematicians appreciated. An impossible figure is like an optical illusion. It is a type of optical illusion. It is possibly the most used type of illusion by Escher. The definition of impossible figure is 2D figure that instantly looks like a 3D object to the human eye even though that figure is not able to exist (is impossible). There is an example of an impossible figure in FIGURE 7. It is not by M.C. Escher.
Screen_shot_2010-02-23_at_10.45.12_AM.png FIGURE 7
When one looks at it, it looks 3D. When it is examined further, one may think, "How can this be?" It is an impossible figure.

Did You Know? (Interesting fact.)

Along with being an artist, Escher was a knite! A man named Alderman Ros was expexted to visit Escher, but Escher did not have compleat knowlege of why. He said to his son Arthur, "In view of the warm weather and my being very busy, I had not dressed up in anything special but was working on a woodcut in my old cord trousers and shirt-sleeves, when Mr. Ros come into the studio together with the town clerk. I had no idea whatever why they had come. I thought they might want to buy one of my prints to adorn a wall in the town hall, or I might be given some commission for the municipality. I put on my old jacket, and after shaking hands asked them to take a seat. Mr. Ros replied that he would rather remain standing. Then he proceeded to tell me that the Mayor was indisposed and that he, Ros, was acting in his stead. I wondered why he had to tell me all this standing up, and again asked them to sit down. Ros refused a second time and said they had to remain standing a little longer. I didn't understand it at all. Possibly he had a boil on his backside? Finally he told me the big news: he was honoured to offer me, in the name of our revered Queen, the Knighthood of the Order of Oranje Nassau. As I watched dumbfounded, he took out a beautiful orange box; out came a silver cross inlaid with enamel. He made some unsuccessful attempts to pin this weighty object onto my chest, but he was too nervous - or the safety pin would not go through my lapels. At any rate, your dad is a knight, even if not of the garter." This happened on April 27th, 1955, so he was fairly popular.

In the End...

Escher is not as known as some other artists or mathematicians. He is no Einstein or Pacaso. He is not someone that the current generation knows off of the top of their heads, but they all know his work. Though his name is not as well known, his works are. They are the most common illutions we know, like in FIGURE 8. People today are still imspired by him. He fooled our eyes on paper, and now everyday people are trying to on other mediums, like in FIGURE 9. He pushed the art boundaries, and subconsciously tied several math concepts in as well.

snakes-white-big.jpg FIGURE 8

238542495_21bb5b1747.jpg FIGURE 9

M.C. Escher died on March 27th 1972 of poor health.