# Pythagorean

Pythagorean means of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras. See:

## Philosophy

• Pythagoreanism an Egyptian-influenced Neo-Platonic philosophy named after the Greek philosopher and mathematician, Pythagoras.

## Sports statistics

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Pythagoras of Samos (Greek: Πυθαγόρας; between 580 and 572 BC–between 500 and 490 BC) was an Ionian (Greek) philosopher[1]
Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics and probably a main inspirational source for Plato and platonism.
In mathematics, the Pythagorean theorem (AmE) or Pythagoras' theorem (BrE) is a relation in Euclidean geometry among the three sides of a right triangle. The theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and
Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2.
A Pythagorean prime is prime number of the form 4n + 1. These are exactly the primes that can be the hypotenuse of a Pythagorean triangle.

The first few Pythagorean primes are
5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113

The Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae (see trigonometric identity#Angle sum and difference identities) it is the basic relation among the
Pythagorean comma, named after the ancient mathematician and philosopher Pythagoras. It is sometimes called a ditonic comma.

Put more succinctly, twelve perfect fifths are not exactly equal to seven perfect octaves, and the Pythagorean comma is the amount of the
Pythagorean tuning is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2. Its name comes from medieval texts which attribute its discovery to Pythagoras, but its use has been documented as long ago as 3500 B.C.
According to legend, Pythagoras discovered the foundations of music by listening to the sounds of four blacksmith's hammers, which produced consonance and dissonance when they were struck simultaneously.
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.