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Enigma of the Universe Viśva-Prahelikä
GEOMETRICAL AND PHILOSOPHICAL ASPECTS OF THEORY OF RELATIVITY
Muni Mahendra Kumar
Non-Euclidean Geometry And Einsteinian Space
Geometry is a branch of mathematics, in which the structure of space is studied. It is a system of mathematical concepts concerning extension. The properties of point, line, plane, angle, etc. are included in it. Ancient Greek mathematician Euclid, (300 B C.) in his monumental work Elements, had laid down the rules and laws of geometry. This is called as 'Euclidean Geometry'. It was based on some self-evident axioms, which were regarded as universal truths. Discovery of Non-Euclidean Geometry
The validity of Euclidean geometry was not questioned till the eighteenth century. Kant went to the extent of supporting his philosophical doctrine that space is a necessary representation a priori, on the basis of Euclidean geometry by considering the geometry of space as independent of experience. But, Saccheri (16671773) was the first man who tried to propound certain laws about 'angles' other than those laid down by Euclid. However he did not succeed fully in his efforts. In any way, the history of non-Euclidean geometry begins with Saccheri. In 1799, mathematician Gauss made a little progress in this field. He showed that it is possible that the sum of the three angles of a triangle, which should be equal to 180° according to the laws of Euclidean geometry, may be less than 180°. To decide this question, Gauss actually measured the triangle having for its vertices Inselsberg, Brocken, and Hoher Hagen (near Gottingen), using methods of the greatest refinement, but the deviation of the sum of the angles from 180° was found to lie within the limits of errors of observation.1 Thus, though it was not definitely decided whether Euclidean or non-Euclidean geometry held in the actual space, the above experiment served a great deal in the development of non-Euclidean geometry.
The honour of the discovery of non-Euclidean geometry went to
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