WORDS NAMED AFTERPYTHAGORAS

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• PYTHAGORAS THEOREM.

• PYTHAGOREAN TRIPLE.

• PYTHAGOREAN EXPECTATION.

• PYTHAGOREAN FIELD.

• PYTHAGOREAN PRIME.

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• PYTHAGOREAN TRIGONOMETRIC IDENTITIES.

• PYTHAGOREAN QUADRAPULE.

• LUTE OF PYTHAGORAS.

PYTHAGORAS THEOREM:

• In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Pythagorean triple:

• A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is aPythagorean triple, then so is (ka, kb, kc) for any positive integer k.

Pythagorean expectation:

• Pythagorean expectation is a formula invented by Bill James to estimate how many games a baseball team "should" have won based on the number of runs they scored and allowed. Comparing a team's actual and Pythagorean winning percentage can be used to evaluate how lucky that team was (by examining the variation between the two winning percentages). The name comes from the formula's resemblance to the Pythagorean theorem.

Pythagoren Field:

• In algebra, a Pythagorean field is a field in which every sum of two squares is a square: equivalently it has Pythagoras number equal to 1. A Pythagorean extension of a fieldF is an extension obtained by adjoining an element √1 + λ2 for some λ in F. So a Pythagorean field is one closed under taking Pythagorean extensions. For any field F there is a minimal Pythagorean field Fpy containing it, unique up to isomorphism, called its Pythagorean closure. The Hilbert field is the minimal ordered Pythagorean field.

Pythgorean prime:

• A Pythagorean prime is a prime number of the form 4n + 1. Pythagorean primes are exactly the odd prime numbers that are the sum of two squares.

Pythagorean trigonometric identities

• The Pythagorean trigonometric identity is atrigonometric identity expressing thePythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations between the sine and cosine functions, from which others may be derived.

Pythagorean quadrapule:

• A Pythagorean quadruple is a tuple of integers a, b, c and d, such that d > 0 and , and is often denoted . Geometrically, a Pythagorean quadruple defines a cuboid with integer side lengths.

Lute of pythagoras:

• The lute of Pythagoras is a self-similar geometric figure made from a sequence of pentagrams.

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