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ესენი უკომენტაროდ:

MC Escher: Artist or Mathematician?

Maurits Cornelius Escher was born on 17th June, 1898 in Leeuwarden, Netherlands. His father was a civil engineer, and he realized at an early age that his son had a liking for art and drawing. This led him to decide to send Escher to study at the School of Architecture and Decorative Arts in Haarlem. However, Escher gave up arcitecture in favor of graphic arts at the age of 21.

Escher spent a number of years travelling in Europe, while his interest in graphics grew. In 1921 he got married and lived in Rome, Italy. At the time, his works depicted landscapes using impossible perspectives.

In the 1930s, Facism in Italy made life impossible for Escher and his family, so they moved to Switzerland. In 1936, Escher embarked on an important journey to the Alhambra in Granada, Spain. The Moorish tilings he saw there fascinated him, and some time after his visit he read Pólya's 1924 paper on plane symmetry groups.

Escher understood the 17 plane symmetry groups described in Pólya's paper, even though he didn't understand the abstract concept of the groups discussed in the paper. Between 1936 and 1942 Escher produced 43 colored drawings with a wide variety of symmetry types while working on possible periodic tilings. He adopted a highly mathematical approach with a systematic study using a notation which he invented himself.

In 1941, Escher returned to the Netherlands, after spending a while in Belgium. His fame slowly spread, and during the 1950s, articles on his work appeared. His works began to be displayed in science museums rather than art galleries.

Escher corresponded with several mathematicians, including Pólya and Coxeter. Escher's relation with mathematics and mathematicians is shown by a number of quotes. First, from a lecture Escher gave in 1953:


... I have often felt closer to people who work scientifically (though I certainly do not do so myself) than to my fellow artists.

In 1958 Escher published Regular Division of the Plane, and in this work he says:


At first I had no idea at all of the possibility of systematically building up my figures. I did not know ... this was possible for someone untrained in mathematics, and especially as a result of my putting forward my own layman's theory, which forced me to think through the possibilities.

Again, in Regular Division of the Plane, Escher writes:


In mathematical quarters, the regular division of the plane has been considered theoretically. ... [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it.

Escher's last years are described as follows:


When Escher's view of the world turned inward he produced his best known puzzling prints, which, art aside, were truly intellecually playful, yet he was not. His life turned inward, he cut himself off and he had few friends. ... He died after a protracted illness...

Escher died on the 27th March, 1972 in Laren, Netherlands.