The theorem can be generalized in various ways: to higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and to objects that are not triangles at all but n-dimensional solids. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean relation: the squared distance between two points equals the sum of squares of the difference in each coordinate between the points. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.
NON EUCLIDEAN GEOMETRY PYTHAGOREAN THEOREM FULL
The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. A full set of Euclidean geometry axioms contains the information about similarity and area that are sufficient to prove the Pythagorean theorem 'synthetically,' that is, directly from the axioms. Johnny Martinez Period 7th Pythagorean Theorem The Pythagorean Theorem also known as Pythagorass theorem is a relation in Euclidean geometry that are the.
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