This is a list of things named after

Pythagoras Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samos, Samian, or simply ; in Ionian Greek; ) was an ancient Ionians, Ionian Ancient Greek philosophy, Greek philosopher and the eponymou ...

, the ancient Greek philosopher, mystic, mathematician, and

music theorist Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (ke ...

Philosophy and mysticism

Pythagoreanism Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the Ancient Greece, ancient Greek col ...

– the system of philosophy of Pythagoras and his followers *

Neopythagoreanism Neopythagoreanism (or neo-Pythagoreanism) was a school of Hellenistic philosophy which revived Pythagorean doctrines. Neopythagoreanism was influenced by middle Platonism and in turn influenced Neoplatonism. It originated in the 1st century BC ...

– a later philosophical system *

Pythagorean cup A Pythagorean cup (also known as a Pythagoras cup, Greedy Cup, Cup of Justice or Tantalus cup) is a practical joke device in a form of a drinking cup, credited to Pythagoras of Samos. When it is filled beyond a certain point, a siphoning effect ...

– a drinking cup that forces its user to imbibe only in moderation *

Pythagorean letter Upsilon (, ; uppercase Υ, lowercase υ; el, ''ýpsilon'' ) or ypsilon is the 20th letter of the Greek alphabet. In the system of Greek numerals, grc, Υʹ, label=none has a value of 400. It is derived from the Phoenician waw . Etym ...

– the Greek letter

upsilon Upsilon (, ; uppercase Υ, lowercase υ; el, ''ýpsilon'' ) or ypsilon is the 20th letter of the Greek alphabet. In the system of Greek numerals, grc, Υʹ, label=none has a value of 400. It is derived from the Phoenician waw . Etym ...

, used as a symbol by the Pythagoreans *

Pythagorean diet Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, ...

– vegetarianism * Pythagorean symbol – the

tetractys The tetractys ( el, τετρακτύς), or tetrad, or the tetractys of the decad is a triangular number, triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row, which is the geometrical repr ...

Pythagorean system Numerology (also known as arithmancy) is the belief in an occult, divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in ...

– the distinctive system of numerology used by the Pythagoreans

Mathematics

Pythagorean theorem 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 t ...

– the statement that the sum of the areas of the squares on the sides of a

right triangle A right triangle (American English) or right-angled triangle (British), or more formally an orthogonal triangle, formerly called a rectangled triangle ( grc, ὀρθόσγωνία, lit=upright angle), is a triangle in which one angle is a right an ...

is the area of the square on the hypotenuse *

Pythagorean triple A Pythagorean triple consists of three positive integers , , and , 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 . A primitive Pythagorean triple is ...

– a set of three positive integers that can occur in the Pythagorean theorem *

Pythagorean quadruple A Pythagorean quadruple is a tuple of integers , , , and , such that . They are solutions of a Diophantine equation and often only positive integer values are considered.R. Spira, ''The diophantine equation '', Amer. Math. Monthly Vol. 69 (1962), ...

- a set of four positive integers that describes the space diagonal of a cuboid. Also known as a Pythagorean box. *

Pythagorean expectation Pythagorean expectation is a sports analytics formula devised by Bill James to estimate the percentage of games a baseball team "should" have won based on the number of runs they scored and allowed. Comparing a team's actual and Pythagorean win ...

– a method of statistical analysis inspired by the Pythagorean theorem *

Pythagorean 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 field F is an extension obtained by adjoining an element \sqrt for some \lamb ...

– in algebra, a

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

in which the sum of two squares is in every case itself a square *

Pythagorean prime A Pythagorean prime is a prime number of the Pythagorean primes are exactly the odd prime numbers that are the sum of two squares; this characterization is Fermat's theorem on sums of two squares. Equivalently, by the Pythagorean theorem, they a ...

– a

prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

of the form 4''n'' + 1 *

Pythagorean trigonometric identity The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae, it is one of the basic relations b ...

– any of several

trigonometric identities In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involvin ...

Pythagorean means In mathematics, the three classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions by Pythagoreans and later generations of Greek mathematicians b ...

– the

arithmetic mean In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The colle ...

, the

geometric mean In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the ...

, and the

harmonic mean In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the recipro ...

Pythagorean addition In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides. According to the Pythagorean theorem, for a triangle with sides a and b, this le ...

– an arithmetic operation arising from the Pythagorean theorem *

Pythagoras's constant The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as \sqrt or 2^, and is an algebraic number. Technically, it should be called the princip ...

– the

square root of 2 The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as \sqrt or 2^, and is an algebraic number. Technically, it should be called the princip ...

Lute of Pythagoras The lute of Pythagoras is a self-similar geometric figure made from a sequence of pentagrams. Constructions The lute may be drawn from a sequence of pentagrams. The centers of the pentagraphs lie on a line and (except for the first and largest o ...

– a geometric figure * Pythagoras tree – a

fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...

geometric figure * Table of Pythagoras, another name for the

Multiplication table In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essenti ...

Music

Pythagorean comma In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher Pythagoras, is the small interval (or comma) existing in Pythagorean tuning between two enharmonically equivalent notes such as C ...

Pythagorean tuning Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2.Bruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: Mc ...

Pythagorean hammers Pythagorean, meaning of or pertaining to the ancient Ionian mathematician, philosopher, and music theorist Pythagoras, may refer to: Philosophy * Pythagoreanism, the esoteric and metaphysical beliefs purported to have been held by Pythagoras * Ne ...

Pythagorean interval In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa.Benson, Donald C. (2003). ''A Smoother Pebble: Mathematical Explorations'', p.56. . " ...

Other

* Pythagoras' Cave, where Pythagoras is said to have hidden from the tyrant

Polycrates Polycrates (; grc-gre, Πολυκράτης), son of Aeaces, was the tyrant of Samos from the 540s BC to 522 BC. He had a reputation as both a fierce warrior and an enlightened tyrant. Sources The main source for Polycrates' life and activit ...

on Mount Kerkis on

Samos Samos (, also ; el, Σάμος ) is a Greek island in the eastern Aegean Sea, south of Chios, north of Patmos and the Dodecanese, and off the coast of western Turkey, from which it is separated by the -wide Mycale Strait. It is also a separate ...

Pythagoreion The Pythagoreion is the archaeological site of the ancient town of Samos in Samos, Greece. It is located in the area of the modern town of Pythagoreio, from which it has got its modern name. The archaeological site contains ancient Greek and Roma ...

, a town on

Pythagoras (crater) Pythagoras is a prominent impact crater located near the northwestern limb of the Moon. It lies just to the northwest of the somewhat larger Babbage. The crater has an oval appearance due to the oblique viewing angle. Only the western face of ...

– a lunar crater *

PythagoraSwitch is a 15-minute Japanese educational television program that has been aired by NHK since April 9, 2002. It encourages augmenting children's "way of thinking" under the supervision of and . A five-minute format called PythagoraSwitch Mini is also ...

– a Japanese educational TV program, which also features sequences showing {{nihongo, ''Pythagorean Devices'', ピタゴラ装置, Pitagora Sōchi. Pythagorean Devices are known in the US as "

Rube Goldberg machine A Rube Goldberg machine, named after American cartoonist Rube Goldberg, is a chain reaction-type machine or contraption intentionally designed to perform a simple task in an indirect and (impractically) overly complicated way. Usually, these machi ...

s", or in Great Britain as "

Heath Robinson William Heath Robinson (31 May 1872 – 13 September 1944) was an English cartoonist, illustrator and artist, best known for drawings of whimsically elaborate machines to achieve simple objectives. In the UK, the term "Heath Robinson cont ...

" contraptions. *

Pythagoras Mechanical Workshop Museum Pythagoras Mechanical Workshop Museum ( sv, Pythagoras industrimuseum) is located in the premises of the earlier engine factory Pythagoras at the town of Norrtälje in the province of Uppland in Sweden. At the museum, production facilities and wo ...

– a building—a former factory—in Sweden *

School of Pythagoras The School of Pythagoras is the oldest building in St John's College, Cambridge, and the oldest secular building in Cambridge, England. It is a Grade 1 listed building. The School of Pythagoras was originally built around 1200, before even the U ...

– the oldest building in

St John's College, Cambridge St John's College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge founded by the House of Tudor, Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corpo ...

Pythagoras ABM Pythagoras is a multi-sided agent-based model (ABM) created to support the growth and refinement of the U.S. Marine Corps Warfighting Laboratory's's Project Albert. Anything with a behavior can be represented as an agent. The interaction of the ...

– an agent-based software model *

Knights of Pythagoras There are many organisations and orders which form part of the widespread fraternity of Freemasonry, each having its own structure and terminology. Collectively these may be referred to as Masonic bodies, Masonic orders or appendant bodies (or ...

– a Masonic body for boys

Pythagoras