HPS391H1 Chapter Notes - Chapter 7: Euclidean Space, Pseudosphere, Ernst Mach
29 Apr 2016
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It is the common geometry that is known today where there is no curvature in space. i. e. a linear space. Example: all the angles of a triangle make up 180 degrees for a euclidean space. Euclid was unable to prove the 5th postulate. Karl friedrich gauss concluded that other geometries other than euclid"s were possible. Nikolai lobachevsky and janos bolyai were the first to formulate a new. The mathematician beltrami used a pseudosphere as a model for non- The pseudosphere has negative curvature, which makes up a triangle with angles less that the sum of 180 degrees. First suggestion that time was the fourth dimension was made by d"alembert. However, time was only used to visualize a higher dimension of space, not the fourth dimension. The rise of popular interest in the new geometries in the 1800s, there were 2 questions regarding the nature of space: 1) curvature of space and non-euclidean geometry, 2) number of dimensions in space.
