Golden Triangle - Penrose Tilings Slide 5-27 Penrose...

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Golden Triangle Slide 5-28: Emmer, plate F3 Emmer, Michele, Ed. The Visual Mind: Art and Mathematics. Cambridge: MIT Press, 1993. The Golden Triangle A golden triangle also called the sublime triangle, is an isoceles triangle whose ratio of leg to base is the golden ratio. It is also an isoceles triangle whose ratio of base to leg is the golden ratio, so there are two types : Type I, acute, and type II, obtuse. A pentagon can be subdivided into two obtuse and one acute golden triangle. Euclid's Construction Euclid shows how to construct a golden triangle. Book IV, Proposition 10 states, "To construct an isoceles triangle having each of the angles at the base the double of the remaining one."
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Unformatted text preview: Penrose Tilings Slide: 5-27: Penrose Tilings. Kappraff, Jay. Connections: The Geometric Bridge between Art & Science. NY: McGraw, 1990. p. 195 One place that the golden triangle appears is in the Penrose Tiling, invented by Roger Penrose, in the late seventies. The curious thing about these tilings is they use only two kinds of tiles, and will tile a plane without repeating the pattern. Making a Penrose Tiling A Penrose tiling is made of two kinds of tiles, called kites and darts. A kite is made from two acute golden triangles and a dart from two obtuse golden triangles, as shown above. Slide 5-29: NCTM C...
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This note was uploaded on 11/05/2011 for the course ARH ARH2000 taught by Professor Karenroberts during the Fall '10 term at Broward College.

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Golden Triangle - Penrose Tilings Slide 5-27 Penrose...

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