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The Road to Reality Study Notes: Difference between revisions
→Chapter 2 An ancient theorem and a modern question
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== Chapter 2 An ancient theorem and a modern question == | == Chapter 2 An ancient theorem and a modern question == | ||
===2.1 The Pythagorean theorem=== | ===2.1 The Pythagorean theorem=== | ||
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===2.4 Hyperbolic geometry: conformal picture=== | ===2.4 Hyperbolic geometry: conformal picture=== | ||
[[File:Escher_circle_limit_1.png|thumb|M. C. Escher’s woodcut Circle Limit I, illustrating the conformal representation of the hyperbolic plane.]] | |||
The topic of questioning fundamental assumptions is taken to a level deeper with the example of Euclid’s fifth postulate and hyperbolic geometry, illustrated with [https://mathstat.slu.edu/escher/index.php/Circle_Limit_Exploration M.C. Escher’s Circle limit I]. The notion that all the black and white fish near the boundary are equal in ‘size’ to the fish near the center starts the section with an interesting point of confusion between our visual perception of Euclidean geometry and the hyperbolic representation. | The topic of questioning fundamental assumptions is taken to a level deeper with the example of Euclid’s fifth postulate and hyperbolic geometry, illustrated with [https://mathstat.slu.edu/escher/index.php/Circle_Limit_Exploration M.C. Escher’s Circle limit I]. The notion that all the black and white fish near the boundary are equal in ‘size’ to the fish near the center starts the section with an interesting point of confusion between our visual perception of Euclidean geometry and the hyperbolic representation. | ||