Question: we will call a noneuclidean geometry a geometry in which...
Question details
We will call a “non-Euclidean geometry” a geometry in which Eu- clid’s five postulates do not all hold.
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(a) Give an example of a non-Euclidean geometry, and explain how you know it is non-Euclidean.
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(b) In most (but not all) non-Euclidean geometries, it’s Euclid’s Fifth pos- tulate that fails to hold. Give another statement that is equivalent to Euclid’s fifth postulate. (You may choose any you like - from the text or by looking this up.) Is this statement true in the geometry you discussed in part (a)? Explain why or why not, drawing some pictures to illustrate.
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(c) Non-Euclidean geometries can be strange places. Explain why the Pythagorean Theorem (as we usually state it) does not hold in spherical geometry.
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