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Impossible Tilings Kabe Moen Washington University in St. Louis Kabe Moen Washington University in St. Louis What is a Tiling ? Kabe Moen Washington University in St. Louis What is a Tiling ? Kabe Moen Washington University in St. Louis What is

  1. Impossible Tilings Kabe Moen Washington University in St. Louis Kabe Moen Washington University in St. Louis

  2. What is a Tiling ? Kabe Moen Washington University in St. Louis

  3. What is a Tiling ? Kabe Moen Washington University in St. Louis

  4. What is a Tiling ? Kabe Moen Washington University in St. Louis

  5. What is a Tiling ? Kabe Moen Washington University in St. Louis

  6. What is a Tiling ? Kabe Moen Washington University in St. Louis

  7. What is a Tiling ? Kabe Moen Washington University in St. Louis

  8. What is a Tiling ? Kabe Moen Washington University in St. Louis

  9. Tilings are the insperation for the some of the artwork of M.C. Escher. Kabe Moen Washington University in St. Louis

  10. We will answer the following questions. How do we make a tiling? What shapes will make a tiling? How can we use tilings to make beautiful artwork? Kabe Moen Washington University in St. Louis

  11. A regular polygon is a shape whose sides and angles are all equal. n ✏ 3 n ✏ 4 n ✏ 5 n ✏ 6 n ✏ 7 n ✏ 8 Kabe Moen Washington University in St. Louis

  12. Jargon: Pentagon Vertex angle side Kabe Moen Washington University in St. Louis

  13. A regular tiling is made up of one regular polygon whose vertices touch. Kabe Moen Washington University in St. Louis

  14. A regular tiling is made up of one regular polygon whose vertices touch. Regular tilings Not regular Kabe Moen Washington University in St. Louis

  15. Can we make regular tiling out of any regular polygon? For example can we make a tiling out of a pentagon? Kabe Moen Washington University in St. Louis

  16. If we drop to word regular we can make tilings out of pentagons. Here are a few. Kabe Moen Washington University in St. Louis

  17. If we drop to word regular we can make tilings out of pentagons. Here are a few. A ! C ! 90 ° A ! 60 °, C ! 120 ° B " E ! 180 ° a ! b, c ! d a ! b, c ! d a ! c Kabe Moen Washington University in St. Louis

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