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Philosophical system based on the teachings of Pythagoras
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans
Pythagoreanism
Greek philosopher (c. 570 – c. 495 BC)
(1455–1522) synthesized Pythagoreanism with Christian theology and Jewish Kabbalah, arguing that Kabbalah and Pythagoreanism were both inspired by Mosaic
Pythagoras
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Topics referred to by the same term
mathematician, philosopher, and music theorist Pythagoras, may refer to: Pythagoreanism, the esoteric and metaphysical beliefs purported to have been held by
Pythagorean
Integer side lengths of a right triangle
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), a well-known
Pythagorean_triple
Method of tuning a musical instrument
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are determined by choosing a sequence of fifths which
Pythagorean_tuning
Sports formula
Pythagorean expectation is a sports analytics formula devised by Bill James to estimate the percentage of games a baseball team "should" have won based
Pythagorean_expectation
Classical averages studied in ancient Greece
Press. p. 163. ISBN 1139444077. Huffman, Carl (2014). A History of Pythagoreanism. Cambridge University Press. p. 168. ISBN 978-1139915984. Virginia Tech
Pythagorean_means
Small interval between musical notes
Pythagorean comma (531441:524288) on C In musical tuning, the Pythagorean comma (or ditonic comma), named after the ancient mathematician and philosopher
Pythagorean_comma
Cup with a central siphon drain
A Pythagorean cup (also known as a Pythagoras cup, greedy cup, cup of justice, anti greedy goblet or Tantalus cup) is a practical joke device in the form
Pythagorean_cup
Length of a line segment
Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient
Euclidean_distance
Set of ancient Greek and Hellenistic religious beliefs
even be considered a single entity, termed "Orphico-Pythagoreanism." The belief that Pythagoreanism was a subset or direct descendant of Orphic religion
Orphism
School of Hellenistic and Roman philosophy
Neopythagoreanism (or neo-Pythagoreanism) was a school of Hellenistic and Ancient Roman philosophy which revived Pythagorean doctrines. Neopythagoreanism
Neopythagoreanism
Musical interval
In musical tuning theory, a Pythagorean interval is a musical interval with a frequency ratio equal to a power of two divided by a power of three, or
Pythagorean_interval
Type of spline curve
In mathematics, a Pythagorean hodograph curve or PH curve is a curve defined by a polynomial parametric equation for which the speed (the derivative of
Pythagorean_hodograph_curve
Ancient Greek astronomer, philosopher and mathematician
of Pontus." From the Stanford Encyclopedia of Philosophy, article "Pythagoreanism". Eusebius, Praeparatio evangelica, Book 15, chapter 58, section 3,
Ecphantus_the_Pythagorean
other Pythagoreans, but accepted death when they reached a bean field because Pythagoreanism forbade touching beans. Ocellus Lucanus was a Pythagorean, but
List of pre-Socratic philosophers
List_of_pre-Socratic_philosophers
Field in which every sum of two squares is a square
a Pythagorean field is a field in which every sum of two squares is a square: equivalently it has a Pythagoras number equal to 1. A Pythagorean extension
Pythagorean_field
Hypothesized astronomical system
occasionally mixes up Platonism with Pythagoreanism. According to Eudemus, a pupil of Aristotle, the early Pythagoreans were the first to find the order of
Pythagorean astronomical system
Pythagorean_astronomical_system
Basic musical interval
functions as a chromatic semitone in a Pythagorean tuning. The Pythagorean limma and Pythagorean apotome are only a Pythagorean comma apart, and may be considered
Semitone
Transmigration of the soul
from early Pythagoreanism is a retrojection, possibly of Nietzschean ideas about the opposition of the Apollonian (associated with Pythagoreanism) and the
Metempsychosis
Four integers where the sum of the squares of three equals the square of the fourth
A Pythagorean quadruple is a tuple of integers a, b, c, and d, such that a2 + b2 + c2 = d2. They are solutions of a Diophantine equation and often only
Pythagorean_quadruple
Hypotenuse of right triangle from its sides
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
Pythagorean_addition
Tiling by squares of two sizes
A Pythagorean tiling or two squares tessellation is a tiling of the Euclidean plane by squares of two different sizes, in which each square touches four
Pythagorean_tiling
Any of the five regular polyhedra
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are
Platonic_solid
school of the Sextii, which was founded by Quintus Sextius and combined Pythagoreanism with Stoicism. Sotion was the teacher of Seneca the Younger, who "sat
Sotion_(Pythagorean)
Natural number
underlies the tetractys, a triangular figure of ten points important in Pythagoreanism. A ten sided polygon is called a decagon. Mathematics portal Weisstein
10
Topics referred to by the same term
Pythagorean tree may refer to: Tree of primitive Pythagorean triples Pythagoras tree (fractal) This disambiguation page lists articles associated with
Pythagorean_tree
Mystical properties of numbers
graffiti dating back to the 6th century BCE. Aristotle wrote that the Pythagorean tradition, founded in the 6th century by Pythagoras of Samos, practiced
Numerology
Country in South Asia
(c. 700–400 BCE) contain the earliest extant verbal expression of the Pythagorean theorem (although very likely it had been known to the Old Babylonians
India
the Pythagorean symbol as exceeding the methodological confines of conventional semiotics. Walter Burkert, Lore and Science in Ancient Pythagoreanism, translated
Androcydes_(Pythagorean)
Musical interval encompassing three half steps
a semiditone (or Pythagorean minor third) is the interval 32:27 (approximately 294.13 cents). It is the minor third in Pythagorean tuning. It arises
Minor_third
Legend about the discovery of musical tuning
ISBN 9780521623711. Burkert, Walter (1972). Lore and Science in Ancient Pythagoreanism, p.375. ISBN 9780674539181. Cited in Christensen 2002, p.143. Markus
Pythagorean_hammers
Concept of rebirth in different physical form
systematized Socrates' thought with concepts he took directly from Pythagoreanism or Orphism. Recent scholars have come to see that Plato has multiple
Reincarnation
Greek philosopher
to southern Italy to study with Archytas and other Pythagoreans. The influence of these Pythagoreans appears to have been significant. According to R.
Plato
Mathematical proof by James Garfield
Garfield's proof of the Pythagorean theorem is an original proof of the Pythagorean theorem discovered by James A. Garfield, the 20th president of the
Garfield's proof of the Pythagorean theorem
Garfield's_proof_of_the_Pythagorean_theorem
5th-century BC Greek philosopher
Stobaeus, Phys. Ecl. i. Reviel Netz,The problem of Pythagorean mathematics in A History of Pythagoreanism, ed C. Huffman, Cambridge UP, 2014: " Pseudo-Alexander
Eurytus_(Pythagorean)
Prime number congruent to 1 mod 4
A Pythagorean prime is a prime number of the form 4 n + 1 {\displaystyle 4n+1} . Pythagorean primes are exactly the odd prime numbers that are the sum
Pythagorean_prime
Ancient philosophical concept
of music. The theory, originating in ancient Greece, was a tenet of Pythagoreanism, and was later developed by 16th-century astronomer Johannes Kepler
Musica_universalis
Musical interval
prefer 45/32 to a small-number interval of about the same width. In the Pythagorean ratio 81/64 both numbers are multiples of 3 or under, yet because of
Tritone
Mathematics of Ancient Greece and the Mediterranean, 5th BC to 6th AD
Netz, Reviel (2014), "The problem of Pythagorean mathematics", in Huffman, Carl A. (ed.), A History of Pythagoreanism, Cambridge University Press, pp. 167–184
Ancient_Greek_mathematics
Unique positive real number which when multiplied by itself gives 2
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. The
Square_root_of_2
Symbol of ten points laid in four rows
As a mystical symbol, it was very important to the secret worship of Pythagoreanism. There were four seasons, and the number was also associated with planetary
Tetractys
Relationship among tones of the chromatic scale
pitch class, but instead overshoots it by a small interval known as the Pythagorean comma. This leads to tuning issues when transposing or modulating, and
Circle_of_fifths
Field of knowledge
and Latin. Traditionally, one of the two main schools of thought in Pythagoreanism was known as the mathēmatikoi (μαθηματικοί)—which at the time meant
Mathematics
Natural number
often representing God or the universe in monotheistic traditions. The Pythagoreans considered the numbers to be plural and therefore did not classify 1
1
President of the United States in 1881
Garfield's aptitude for mathematics extended to his own proof of the Pythagorean theorem, published in 1876, and his advocacy of using statistics to inform
James_A._Garfield
Philosophical concept of a most basic substance, or supreme being
to a most basic or original substance. As originally conceived by the Pythagoreans, the Monad is therefore Supreme Being, divinity, or the totality of all
Monad_(philosophy)
Mathematical tree of integer right triangles
primitive Pythagorean triples is a mathematical tree in which each node represents a primitive Pythagorean triple and each primitive Pythagorean triple is
Tree of primitive Pythagorean triples
Tree_of_primitive_Pythagorean_triples
Relation between sine and cosine
The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric
Pythagorean trigonometric identity
Pythagorean_trigonometric_identity
Dialogue by Plato on the immortality of the soul
impiety. Many of the key characters in the dialogue are associated with Pythagoreanism, a religious and philosophical doctrine that flourished early 5th century
Phaedo
Polygonal curve made from right triangles
geometry, the spiral of Theodorus (also called the square root spiral, Pythagorean spiral, or Pythagoras's snail) is a spiral composed of right triangles
Spiral_of_Theodorus
Relation between the side lengths and altitude of a right triangle
In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem or the upside down Pythagorean theorem) is as follows: Let
Inverse_Pythagorean_theorem
Musical interval
41-ET, 53-ET, and 72-ET. Conversely, in twelve-tone equal temperament, Pythagorean tuning, and meantone temperament (including 19-ET and 31-ET) all major
Major_second
Ancient Greek pythagorean philosopher
Philosophy. London: Search Press, 1946. Guthrie, W.K.C. "Pythagoras and Pythagoreanism," in Encyclopedia of Philosophy. Vol. 7. Edited by Paul Edwards. NY:
Damo_(philosopher)
Most beautiful woman in Greek mythology
Greek word Σελήνη (Selēnē), meaning "Moon, goddess of the moon". One Pythagorean source claimed that Helen had originally come from a colony on the moon
Helen_of_Troy
Study of general and fundamental questions
Mohism Chinese naturalism Taoism Yangism Greco-Roman Pre-Socratic Ionians Pythagoreans Eleatics Atomists Sophists Cyrenaics Cynicism Eretrian school Megarian
Philosophy
Besides Euclid's formula, many other formulas for generating Pythagorean triples have been developed. Euclid's, Pythagoras' and Plato's formulas for calculating
Formulas for generating Pythagorean triples
Formulas_for_generating_Pythagorean_triples
Every natural number can be represented as the sum of four integer squares
Lagrange's four-square theorem, also known as Bachet's conjecture, states that every nonnegative integer can be represented as a sum of four non-negative
Lagrange's four-square theorem
Lagrange's_four-square_theorem
Third planet from the Sun
3402/tellusa.v26i1-2.9731. Kahn, Charles H. (2001). Pythagoras and the Pythagoreans: A Brief History. Indianapolis, IN and Cambridge, England: Hackett Publishing
Earth
5th-century BC Pythagorean philosopher
50–51. Springer. Walter Burkert (1972), Lore and Science in Ancient Pythagoreanism, page 459. Harvard University Press. Plato, Theaetetus, 147d ff. Thomas
Hippasus
American musician
mathematical concepts. He has written several compositions using a non-Pythagorean scale based on logarithms. He has also incorporated prime numbers and
Robert_Schneider
Games Nemean Games Pythian Games Isthmian Games Philosophy Schools Pythagoreanism Neopythagoreanism Platonism Middle Platonism Neoplatonism Philosophers
Lists of Greek mythological figures
Lists_of_Greek_mythological_figures
Book about right triangles by Wacław Sierpiński in 1954
Pythagorean Triangles is a book on right triangles, the Pythagorean theorem, and Pythagorean triples. It was originally written in the Polish language
Pythagorean_Triangles
Natural number
the union of the physical (number 4) with the spiritual (number 3). In Pythagorean numerology the number 7 means spirituality. The number seven had mystical
7
Twentieth letter in the Greek alphabet
writer Persius wrote in Satire III: and the letter which spreads out into Pythagorean branches has pointed out to you the steep path which rises on the right
Upsilon
Musical interval
intonation there is both a 16:9 "lesser just minor seventh", also called the "Pythagorean small minor seventh",(Play) equivalent to two perfect fourths stacked
Minor_seventh
Result in Fourier analysis
sum of squares of the amplitudes). Geometrically, it is a generalized Pythagorean theorem for inner-product spaces (which can have an uncountable infinity
Parseval's_identity
Triangle containing a 90-degree angle
integers, the triangle is called a Pythagorean triangle and its side lengths are collectively known as a Pythagorean triple. The relations between the
Right_triangle
Right triangle with a feature making calculations on the triangle easier
know the Pythagorean theorem, but that "there is no evidence that they used it to construct right angles". The following are all the Pythagorean triple
Special_right_triangle
Greek philosopher (c. 470–399 BC)
Anaximander Anaximenes Heraclitean Heraclitus Cratylus Diogenes Italian Pythagorean Pythagoras Hippasus Philolaus Archytas Lamiskos Alcmaeon Brontinus Theano
Socrates
Greek philosopher (c. 470 – c. 385 BC)
mixes up Platonism with Pythagoreanism. Alcmaeon of Croton Apeiron Nicomachus Parmenides Protrepticus (Aristotle) Pythagoreans "The most likely date for
Philolaus
Greek Neopythagorean philosopher (c.15–100)
2nd century the satirist Lucian of Samosata was a sharp critic of Neo-Pythagoreanism. After AD 180 he wrote a pamphlet wherein he attacked Alexander of Abonoteichus
Apollonius_of_Tyana
Hypothetical planet on the other side of the Sun from Earth
"Central Fire" was developed in the 5th century BC and attributed to the Pythagorean philosopher Philolaus. Philolaus' universe moved "the earth from the
Counter-Earth
Dios was an ancient Greek philosopher of uncertain date. Certain Pythagorean writings on aesthetics are ascribed to him. Two fragments found in Stobaeus
Dios_(philosopher)
Musical tuning system
temperaments; that is, a variety of tuning systems constructed, similarly to Pythagorean tuning, as a sequence of equal fifths, both rising and descending, scaled
Meantone_temperament
Second planet from the Sun
Penguin. pp. 15–16. Burkert, Walter (1972). Lore and Science in Ancient Pythagoreanism. Harvard University Press. p. 307. ISBN 978-0-674-53918-1. Archived
Venus
Musical scale set of twelve pitches
decimal): where 256⁄243 is a diatonic semitone (Pythagorean limma) and 2187⁄2048 is a chromatic semitone (Pythagorean apotome). In 5-limit just intonation the
Chromatic_scale
theorist. Pythagoreanism – the system of philosophy of Pythagoras and his followers Neopythagoreanism – a later philosophical system Pythagorean cup – a
List of things named after Pythagoras
List_of_things_named_after_Pythagoras
Ancient Greek goddess
Games Nemean Games Pythian Games Isthmian Games Philosophy Schools Pythagoreanism Neopythagoreanism Platonism Middle Platonism Neoplatonism Philosophers
Athena
Set of integers, the lengths of the sides of a triangle with a 60° angle
Similar to a Pythagorean triple, an Eisenstein triple (named after Gotthold Eisenstein) is a set of integers which are the lengths of the sides of a triangle
Eisenstein_triple
Supreme being in theistic belief systems
the Universe. God is often viewed as the cause of all that exists. For Pythagoreans, Monad variously referred to divinity, the first being or an indivisible
God
Measurement of a string instrument
The scale length of a string instrument is the maximum vibrating length of the strings that produce sound, and determines the range of tones that string
Scale length (string instruments)
Scale_length_(string_instruments)
Natural number
Sequences. OEIS Foundation. "Pythagorean triples". mathworld.wolfram.com. Tobin-Campbell, Christopher. "Systems of Pythagorean Triples" (PDF). www.whitman
305_(number)
Generalization of Pythagorean theorem
\beta .\end{aligned}}} The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if γ {\displaystyle
Law_of_cosines
Group of Vedic Sanskrit texts
including an approximation of the square root of 2 and the statement of the Pythagorean theorem. Baudhayana's Śrauta sūtras related to performing Vedic sacrifices
Baudhayana_sutras
Ethnoreligious group of the Levant
Christianity, Gnosticism, Neoplatonism, Zoroastrianism, Manichaeism, and Pythagoreanism.[page needed] This has led to the development of a distinct and secretive
Druze
Circle with radius of one
legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, x and y satisfy the equation x 2 + y 2 = 1. {\textstyle x^{2}+y^{2}=1
Unit_circle
Natural number
sequence. 265 is the 7th number to be the hypotenuse for two separate Pythagorean Triples. The other two values would be 23 and 264 or 96 and 247. 265
265_(number)
Interval in music
The Pythagorean ditone is the major third in Pythagorean tuning, which has an interval ratio of 81:64, which is 407.82 cents. The Pythagorean ditone
Ditone
Texts belonging to the Śrauta ritual
statements of the Pythagorean theorem, both in the case of an isosceles right triangle and in the general case, as well as lists of Pythagorean triples. In
Shulba_Sutras
Numerical symbol
Gerbert of Aurillac marked triples of columns with an arc (called a "Pythagorean arc"), when using his Hindu–Arabic numeral-based abacus in the 10th century
Decimal_separator
Dissonant musical interval
but variable magnitudes) produced by other tuning systems, including Pythagorean and most meantone temperaments. When the twelve notes within the octave
Wolf_interval
Founding Father, U.S. president from 1797 to 1801
suggested that the Christian Trinity was likely a "fabrication" derived from Pythagorean and Platonic philosophies rather than divine revelation. He further argued
John_Adams
Longest side of a right-angled triangle, the side opposite of the right angle
legs or catheti. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse
Hypotenuse
Problem in physics and astronomy
In physics and astronomy, Euler's three-body problem is to solve for the motion of a particle that is acted upon by the gravitational field of two other
Euler's_three-body_problem
4th-century BC Greek philosopher, mathematician, astronomer and statesman
Google books. Horky, P.S. (2021). "Archytas: Author and authenticator of Pythagoreanism". In Macris, C.; Dorandi, T.; Brisson, L. (eds.). Pythagoras Redivivus:
Archytas
Natural number
Greek goddess Hecate and the Triple Goddess of Wicca. Pythagoras and the Pythagorean school highlighted that the number 3, which they called triad, is the
3
Roman philosopher and writer
their esoteric Pythagoreanism, into which Nigidius incorporated Stoic elements. Jerome called him Pythagoricus et magus, a "Pythagorean and mage," and
Nigidius_Figulus
Early Christian and Jewish religious systems
called æons. According to Hippolytus, this view was inspired by the Pythagoreans, who called the first thing that came into existence the Monad, which
Gnosticism
PYTHAGOREANISM
PYTHAGOREANISM
PYTHAGOREANISM
PYTHAGOREANISM
Girl/Female
Afghan, Arabic, Muslim
Memory
Boy/Male
Hindu
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Thai
Very Big; Gazelle
Girl/Female
Arabic, Muslim
Pure
Girl/Female
Australian, French, Turkish
Red Ornament
Girl/Female
Tamil
Avani | அவநீ, அபநீÂ
Earth
Female
English
English variant spelling of German Kristen, CHRISTEN means "believer" or "follower of Christ."
Girl/Female
Muslim/Islamic
Bright shining
Boy/Male
Tamil
Mrigendra | மரகேநà¯à®¤à¯à®°
Lion
Boy/Male
Gujarati, Hindu, Indian, Malayalam, Marathi
King of Braj Land
PYTHAGOREANISM
PYTHAGOREANISM
PYTHAGOREANISM
PYTHAGOREANISM
PYTHAGOREANISM
n.
The doctrines of Pythagoras or the Pythagoreans.