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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), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A triangle whose side lengths are a Pythagorean triple is a right triangle and called a…

Elementary properties of primitive Pythagorean triples, Spinors and the modular group & Special cases and related equations

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Elementary properties of primitive Pythagorean triples

DivisibleEvenEuclid's formulaPrimes of the form 4n + 1OEIS
21 related topics

Spinors and the modular group

Square matrixSymmetricDeterminantRankLinear algebra
20 related topics

Special cases and related equations

ProclusEuclid's ElementsPythagorasSimilarDiophantus II.VIII
18 related topics

Geometry of Euclid's formula

Rational pointUnit circleCartesian planeCoprime integersParametric equation
15 related topics

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Overview

Generating a triple

Elementary properties of primitive Pythagorean triples

Geometry of Euclid's formula

Related triangle geometry

Pythagorean triangles in a 2D lattice

Enumeration of primitive Pythagorean triples

Spinors and the modular group

Parent/child relationships

Relation to Gaussian integers

Distribution of triples

Special cases and related equations

Generalizations

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Pythagorean triple

Nodes148
Edges147
Triples248
Avg. degree1.99
Density0.013514
Components1

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Pythagorean triple

Top relations

related to References · 70
Pythagorean triple → Alperin, Amer, American Mathematical Monthly, Andrzej, Artemas, Berggren, Books, Calvin, Centrum Amsterdam Afd, Cite, CiteSeerX, Company, Dan, Darryl, Date, Dover Publications, DS/0406512, Dutch, Elementary Introduction, Elementär Matematik
related to External links · 40
Pythagorean triple → Arithmetic Progressions, Clifford Algebras, Consequences, EMS Press, Encyclopedia, Eric, Euclid's Parameterization, Friendly Introduction, Incircle, Interactive Applet, Interactive Calculator, Interactive Calculators, ISBN, Joseph, Lee, Mathematics, MathWorld, Miscopied QuadraticDiscussion, New Species, NJ
related to General properties · 20
Pythagorean triple → A008846, Any, At, Diophantine, Euclid's, Exactly, Fermat's, However, Neither, Niven's, No, OEIS, Only, Pythagorean, See, The, There, Therefore, This, Tree
related to Special cases · 16
Pythagorean triple → According, Euclid's, Every, Fermat, For, Here, If, In, More, Pythagorean, Such, Such Pythagorean, The, There, They, This
related to Pythagorean triangles in a 2D lattice · 10
Pythagorean triple → A093536, A225760, Any Pythagorean, As, Cartesian, OEIS, Pick's, Pythagorean, The, Three
related to Heronian triangle triples · 9
Pythagorean triple → Every Pythagorean, Here, Heronian, If, Not, Pythagorean, The, The Heronian, With
related to Parent/child relationships · 8
Pythagorean triple → Berggren, By, In, Pythagorean, Starting, T1, T2, T3
related to Related triangle geometry · 7
Pythagorean triple → As, Descartes, Moreover, Pythagorean, Thales, The, When
related to Distribution of triples · 6
Pythagorean triple → Different, In, Pythagorean, There, Whenever, Within
related to Enumeration of primitive Pythagorean triples · 6
Pythagorean triple → By Euclid's, Hence, It, One, Pythagorean, The

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Important terminology

pythagorean displaystyle triple primitive triples integers integer formula one even triangle euclid's right odd hypotenuse coprime every number positive sides

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Pythagorean tripleis aright triangle and called a Pythagorean triangle.A primitive Pythagorean triple is one in which a0.90text
Pythagorean tripleis aHeronian triple0.90text
Cantor's pairing functioninstance ofand mapped to an integer using a pairing function0.80text
Pythagorean triplerelated to A variantThe0.60section
Pythagorean triplerelated to A variantEuclid's0.60section
Pythagorean triplerelated to A variantIf0.60section
Pythagorean triplerelated to A variantPythagorean0.60section
Pythagorean triplerelated to A variantConversely0.60section
Pythagorean triplerelated to Almost-isosceles Pythagorean triplesNo Pythagorean0.60section
Pythagorean triplerelated to Almost-isosceles Pythagorean triplesThere0.60section
Pythagorean triplerelated to Application to cryptographyPrimitive Pythagorean0.60section
Pythagorean triplerelated to Distribution of triplesThere0.60section

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