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non-Euclidean geometry

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                NON-EUCLIDEAN GEOMETRY                  Every mathematics student to professor everyone heard the name of Euclid. He is famous for his contribution to the mathematics. One of his great contribution is Euclidean geometry. That we study whole our school life, that all based  on Euclid postulate and axioms that he write on his famous book "The Elements", that book has13 chapters based on his geometry.     And the great thing you know before 19th century mathematicians believe that Euclid geometry is god's word so no another geometry not exist, and but some mathematicians are believe some of Euclid postulate is can derive from other, so some are trying to prove but many tries and fail.      In 19th century  János Bolyai  and  Nikolai Ivanovich Lobachevsky  (separately) thought that instead of proving one of them imply from another we can make or study geometry that not follow some of Euclid postulates .  Before go on into non-Euclidean geometry we first see E