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Lobachevski, Nikolai Ivanovich

euclidean geometry line fifth

[loba chef skee] (1793–1856) Russian mathematician: discovered one of the first non-Euclidean geometries.

Lobachevski’s father died when he was about 6, and after his mother had moved the family to Kazan he attended the new university there in 1807. He joined its staff in 1814 and in 1827 became its rector. He was honoured by his government, but in 1846 fell into disfavour for reasons which are unclear; he had done much for his university and his country.

From 1827 onwards Lobachevski developed the first non-Euclidean geometry to be published, although J Bolyai (1802–60) was doing similar work at the same time and had done so decades before, but without publication fifth postulate (‘axiom XI’) could not be proved. The fifth postulate is that, given a straight line and a point, just one straight line can be drawn in their plane passing through the point and never meeting the other line. Euclidean geometry was widely thought adequate to describe the world and the universe. Lobachevskian geometry accepts Euclidean postulates, except the fifth, and occurs on a curved surface with two lines always meeting in one direction and diverging in the other. The angles of a triangle no longer add up to two right angles but sum to less than that. Lobachevski’s work was only widely accepted as important when general theory of relativity showed that the geometry of space-time is non-Euclidean; it also prepared the way for the systematic exploitation of non-Euclidean geometry . Euclidean geometry is now seen as a special case, adequate for all everyday purposes, within a more general system.

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