In this paper, I intend to explain the basis of M.C. Escher and show a couple of examples of his work. 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 tiling. 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. MC Escher, who was born in Leeuwarden, Holland in 1898, created unique and fascinating works of art that explore and exhibit a wide range of mathematical ideas. Among his greatest admirers were mathematicians, who recognized in his work an extraordinary visualization of mathematical principles. This was most amazing seeing that Escher had no not learned math beyond secondary school. As his work developed, he drew great inspiration from the mathematical ideas he read about, often working directly from structures in plane and projective geometry, and eventually capturing the essence of non-Euclidean geometries, as we will see below. He was also fascinated "impossible" figures, and used an idea of Roger Penrose's to develop many intriguing works of art. The way MC worked changed the way we view many types of artwork and in a great sense it opens our eyes to visualize many different views on the world we live in and how math itself can actually be
Escher used these basic patterns in his tessellations; applying what we know as reflections, glide reflections, translations, and rotations to obtain a greater variety of patterns. He also elaborated these...
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