Euclidean geometry is the geometry described by the mathematician Euclid (ca 300 BC) in his landmark work Elements.^{[1]} As head librarian at the famed Library of Alexandria, Euclid had access to the best minds of the ancient world.
Euclid's main contribution to mathematics was an axiomatic approach. The axiomatic approach involves basic statements called axioms that are taken to be true without proof. All other conclusions are proved from these axioms.
In his book Elements, Euclid described five axioms:
From these five axioms, all other theorems in Euclidean geometry are proved. In general, Euclidean geometry is distinguished from non-Euclidean geometry by the fifth postulate, also called the parallel postulate. In attempting to prove that the fifth postulate was not necessary to Euclidean geometry, mathematicians discovered that, if the fifth postulate was not included, other geometries different from Euclidean geometry were possible.
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