Impossible Tilings Kabe Moen Washington University in St. Louis - - PowerPoint PPT Presentation

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Impossible Tilings Kabe Moen Washington University in St. Louis - - PowerPoint PPT Presentation

Dec 06, 2023 1.33k likes •1.56k views

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

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Impossible Tilings

Kabe Moen Washington University in St. Louis

Kabe Moen Washington University in St. Louis

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What is a Tiling?

Kabe Moen Washington University in St. Louis

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What is a Tiling?

Kabe Moen Washington University in St. Louis

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What is a Tiling?

Kabe Moen Washington University in St. Louis

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What is a Tiling?

Kabe Moen Washington University in St. Louis

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What is a Tiling?

Kabe Moen Washington University in St. Louis

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What is a Tiling?

Kabe Moen Washington University in St. Louis

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What is a Tiling?

Kabe Moen Washington University in St. Louis

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Tilings are the insperation for the some of the artwork of M.C. Escher.

Kabe Moen Washington University in St. Louis

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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

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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

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Jargon: Pentagon

angle side Vertex

Kabe Moen Washington University in St. Louis

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A regular tiling is made up of one regular polygon whose vertices touch.

Kabe Moen Washington University in St. Louis

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A regular tiling is made up of one regular polygon whose vertices touch. Regular tilings Not regular

Kabe Moen Washington University in St. Louis

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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

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If we drop to word regular we can make tilings out of

  • pentagons. Here are a few.

Kabe Moen Washington University in St. Louis

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If we drop to word regular we can make tilings out of

  • pentagons. Here are a few.

A ! C ! 90° a ! b, c ! d A ! 60°,C ! 120° a ! b, c ! d B " E ! 180° a ! c Kabe Moen Washington University in St. Louis