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Unformatted text preview: and the ratio of straight lines drawn similarly from their centers of gravity to the axes of rotation. Non-Euclidean Geometry Attempts to prove the parallel postulate. Why were they undertaken? What was their common pitfall? Saccheri ( 1700) and his quadrilaterals. (Hypotheses of the acute, obtuse, right angle.) Legendre and his proof of the parallel postulate. Questioning the parallel postulate. Philosophical issues Strict adherence to only axioms and postulates Logical necessity versus empirical justication How to give a proof of the (relative) consistency of non-Euclidean geometry. Models Reinterpretation of terms Discoveries of the properties of Non-Euclidean Geometry Apparently discovered independently by Lobachevskii (,1829), Janos Bolyai (1823,1832), and Gauss (1824,)....
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This note was uploaded on 12/29/2011 for the course MATH 378 taught by Professor Wen during the Fall '10 term at SUNY Stony Brook.
- Fall '10