Pythagorean
Encyclopedia
Pythagorean means of or pertaining to the ancient Ionia
n mathematician, philosopher, and music theorist Pythagoras
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Ionia
Ionia is an ancient region of central coastal Anatolia in present-day Turkey, the region nearest İzmir, which was historically Smyrna. It consisted of the northernmost territories of the Ionian League of Greek settlements...
n mathematician, philosopher, and music theorist Pythagoras
Pythagoras
Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...
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Philosophy
- PythagoreanismPythagoreanismPythagoreanism was the system of esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics. Pythagoreanism originated in the 5th century BCE and greatly influenced Platonism...
is a term used for the esoteric and metaphysical beliefs purported to have been held by Pythagoras. - Neo-Pythagoreanism was a school of philosophy reviving Pythagorean doctrines that became prominent in the 1st and 2nd centuries AD.
- Pythagorean diet was the name for vegetarianism prior to the nineteenth century
Mathematics
- Pythagorean theoremPythagorean theoremIn mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...
- Pythagorean triplePythagorean tripleA Pythagorean triple consists of three positive integers a, b, and c, such that . Such a triple is commonly written , and a well-known example is . If is a Pythagorean triple, then so is for any positive integer k. A primitive Pythagorean triple is one in which a, b and c are pairwise coprime...
- Pythagorean primePythagorean primeA 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...
- Pythagorean trigonometric identityPythagorean trigonometric identityThe Pythagorean trigonometric identity is a trigonometric identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one the basic relations between the sine and cosine functions, from which all others may be derived.-Statement of...
- Pythagorean approximation
- Table of Pythagoras, another name for the Multiplication tableMultiplication tableIn mathematics, a multiplication table is a mathematical table used to define a multiplication operation for an algebraic system....