Unformatted text preview: and the ratio of straight lines drawn similarly from their centers of gravity to the axes of rotation.” NonEuclidean 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 justi±cation ⋆ How to give a proof of the (relative) consistency of nonEuclidean geometry. · Models · Reinterpretation of terms ◦ Discoveries of the properties of NonEuclidean Geometry ⋆ Apparently discovered independently by Lobachevskii (,1829), Janos Bolyai (1823,1832), and Gauss (1824,)....
View
Full Document
 Fall '10
 wen
 Geometry, NonEuclidean Geometry, Euclidean geometry, Euclid, Parallel postulate

Click to edit the document details