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The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras, [216] [214] [217] [218] but he may have been the first to introduce it to the Greeks. [219] [217] Some historians of mathematics have even suggested that he—or his students—may have constructed the first proof. [220]
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.
The Pythagorean theorem was referenced in Arabic manuscripts. [83] Scholars in the Arabic world displayed a strong interest in Pythagorean concepts. In the 10th century Abu al-Wafa' Buzjani discussed multiplication and division in a treatise on arithmetic for business administrators in reference to Nicomachus.
Pythagorean, meaning of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras, may refer to: Philosophy.
Pythagorean quadruple - a set of four positive integers that describes the space diagonal of a cuboid. Also known as a Pythagorean box. Pythagorean expectation – a method of statistical analysis inspired by the Pythagorean theorem; Pythagorean field – in algebra, a field in which the sum of two squares is in every case itself a square
The study of the Pythagorean means is closely related to the study of majorization and Schur-convex functions. The harmonic and geometric means are concave symmetric functions of their arguments, and hence Schur-concave, while the arithmetic mean is a linear function of its arguments and hence is both concave and convex.
Geometrically, the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. [1] The fraction 99 / 70 (≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator.
In mathematics, the Pythagoras number or reduced height of a field describes the structure of the set of squares in the field. The Pythagoras number p ( K ) of a field K is the smallest positive integer p such that every sum of squares in K is a sum of p squares.