Penrose began to work on the problem of whether a set of shapes could be found which would tile a surface but without generating a repeating pattern (known as quasi-symmetry). While there, he began playing with geometric puzzles and tessellations. While most of his work pertains to relativity theory and quantum physics, he is fascinated with a field of geometry known as tessellation, the covering of a surface with tiles of prescribed shapes. Roger Penrose, a professor of mathematics at the University of Oxford in England, pursues an active interest in recreational math which he shared with his father. Some people say that he is the expert in recreational math. Tessellation Artist/Mathematician Roger Penrose His products look excellent for any classroom teacher. Fathauer now promotes mathematical art at exhibitions and conferences. Later in 1993 he founded his own company called Tessellations to produce tessellation puzzles and offer them for sale. Robert Fathauer received his doctorate from Cornell University in Electrical Engineering and joined the research staff of the Jet Propulsion Laboratory in Pasadena, California. Both disciplines appeal to me for these reasons, and it seems natural to combine them." Conversely, art is the discipline where beauty is the traditional goal, but art also strives to get at deep truths. At the same time, there is great beauty and elegance in mathematics. It's the one discipline where results can be proven to be true. Fathauer, "if there's anything one can be certain of in this world it's mathematics. Robert has an interest in mathematics and art and has been a great fan of Escher. Robert Fathauer, born in 1960, creates his tessellations using a computer. Robert Fathauer stands next to his art, "Twice iterated Knot." He entered this in the American Mathematical Society Exhibition. Another Tessellation Artist, Robert Fathauer Technically, the shapes at the top and bottom of his woodcut are no longer tessellations because they spread apart and the space around them no longer resemble fish or ducks. The tessellations are the fish shapes in white next to the duck shapes in white.
Escher shows us that reality is wondrous, comprehensible and fascinating.Įxamining one of his woodcuts, Sky & Water I (left above), we see fish in the sea and as you go up, the space between the fish transform into black ducks. In his work we recognize his keen observation of the world around us and the expressions of his own fantasies. His art continues to amaze and wonder millions of people all over the world. He played with architecture, perspective and impossible spaces. Many of these sketches he would later use for various other lithographs and/or woodcuts and wood engravings. During these 11 years, Escher would travel each year throughout Italy, drawing and sketching for the various prints he would make when he returned home. They settled in Rome, where they stayed until 1935. After finishing school, he traveled extensively through Italy, where he met his wife Jetta Umiker. He was born in Leeuwarden, the Netherlands, as the fourth and youngest son of a civil engineer. Escher illustrated books, designed tapestries, postage stamps and murals. Like some of his famous predecessors, - Michelangelo, Leonardo da Vinci, Dürer and Holbein-, M.C. Escher, during his lifetime, made 448 lithographs, woodcuts and wood engravings and over 2000 drawings and sketches. What made Escher's pictures so appealing was that he used tessellations to create optical illusions. He is most famous for his so-called "impossible structures", such as Ascending and Descending, Relativity, his Transformation Prints, such as Metamorphosis I, Metamorphosis II and Metamorphosis III, Sky & Water I or Reptiles. He created visual riddles, playing with the pictorially logical and the visually impossible. His art is enjoyed by millions of people all over the world. Maurits Cornelis Escher (1898-1972) is a graphic artist known for his art tessellations. "A collection of plane figures that fills the plane with no overlaps and no gaps." Īdvertisement "Designs featuring animals, birds, etc, which can fill the page, without over-lapping, to form a pattern." "To form into a mosaic pattern, as by using small squares of stone or glass." "A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps."
0 kommentar(er)
