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In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle ) is equal to the sum of the areas of the squares on the other two sides.
A superpythagorean field F is a formally real field with the property that if S is a subgroup of index 2 in F ∗ and does not contain −1, then S defines an ordering on F. An equivalent definition is that F is a formally real field in which the set of squares forms a fan. A superpythagorean field is necessarily Pythagorean. [12]
[5] [6] [7] The earliest sources on Pythagoras's life are brief, ambiguous, and often satirical. [4] [8] [9] The earliest source on Pythagoras's teachings is a satirical poem probably written after his death by the Greek philosopher Xenophanes of Colophon (c. 570 – c. 478 BC), who had been one of his contemporaries.
Animation demonstrating the smallest Pythagorean triple, 3 2 + 4 2 = 5 2. A Pythagorean triple consists of three positive integers a, b, and c, such that a 2 + b 2 = c 2.Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5).
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Much of the surviving sources on Pythagoras originated with Aristotle and the philosophers of the Peripatetic school, which founded historiographical academic traditions such as biography, doxography and the history of science. The surviving 5th century BC sources on Pythagoras and early Pythagoreanism are void of supernatural elements, while ...
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Jimmy Butler of the Miami Heat is reportedly ready for a trade to a contending team, though he has not formally asked for a trade. (Photo by Rich Storry/Getty Images) (Rich Storry via Getty Images)