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Nicolai Ivanovich Lobachevsky (December 1, 1792 - February 24, 1856)
-Developed a form of non-Euclidean geometry in which Euclid's Fifth Postulate does not hold (hyperbolic geometry). -Found that the sum of the angles in a triangle must be less than 180 degrees in hyperbolic geometry. -Showed that Euclidean spherical trigonometry is valid in hyperbolic geometry. -Developed method for approximating the roots of algebraic equations which is known as the Dandelin-Graffe method.