He continued trying to devise a tessellation that would never repeat itself horizontally or vertically. The shape Escher created, based on the one by Penrose and the basis for his final drawing The search for a non-repeating tessellation In this two-part documentary Roger Penrose talks about his relationship to Escher. It went against the belief he had held for many years that a tessellation, by means of various reflections and rotations, could be continued indefinitely. In the letter, Escher expressed his astonishment that the forms only fitted together in one way. Escher accepted the challenge and puzzled over it for a while, until a few weeks later he was able to send Penrose a letter outlining the solution. The mathematician challenged the graphic artist to solve the puzzle. The shapes fitted together in many ways, but there was only one unique way in which they could be combined to create a tessellation containing all the puzzle pieces. Two sides of the rhombus had been modified by cutting out a trapezoidal shape with angles of 60 and 120 degrees and positioning it on the other sides. It consisted of a series of identical geometric shapes based on a rhombus. Penrose received a print from Escher and in return he gave his host a wooden puzzle. Throughout his career Penrose was fascinated by tessellations, a fascination that he shared with Escher. They started an exchange of letters that would lead to the print Ascending and Descending in 1960. The two had got to know each other after Penrose saw work by Escher during the International Mathematical Congress in 1954. In 1962 the British mathematician Roger Penrose travelled to the Netherlands and he visited Escher in his house in Baarn. 137), India ink and watercolor on paper, May 1971 Escher, Regular division drawing with ghosts (no.
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