Class 9 Maths Euclid Geometry Non Euclidean Geometry

Non Euclidean Geometry:

All the attempts to prove Euclid’s fifth postulate using the first 4 postulates failed. But they led to the discovery of several other geometries, called non-Euclidean geometries. Now the geometry of the universe we live in has been shown to be a non-Euclidean geometry. In fact, it is called spherical geometry. In spherical geometry, lines are not straight. They are parts of great circles (i.e., circles obtained by the intersection of a sphere and planes passing through the centre of the sphere).    As per fist postulate of Euclid, lines AN & BN should not meet, but in the image below, these lines meet at point N. It has been proved that Euclidean geometry is valid only for the figures in the plane. On the curved surfaces, it fails.

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