Definitions for Pythagorean triple
pythagore·an triple

WiktionaryRate this definition:0.0 / 0 votes

1. Pythagorean triplenoun

   A set of three positive integers a, b and c, where a = b + c

WikipediaRate this definition:0.0 / 0 votes

1. 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), and 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 primitive Pythagorean triple is one in which a, b and c are coprime (that is, they have no common divisor larger than 1). For example, (3, 4, 5) is a primitive Pythagorean triple whereas (6, 8, 10) is not. A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle, and is necessarily a right triangle. The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a 2 + b 2 = c 2 {\displaystyle a^{2}+b^{2}=c^{2}} ; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples. For instance, the triangle with sides a = b = 1 {\displaystyle a=b=1} and c = 2 {\displaystyle c={\sqrt {2}}} is a right triangle, but ( 1 , 1 , 2 ) {\displaystyle (1,1,{\sqrt {2}})} is not a Pythagorean triple because 2 {\displaystyle {\sqrt {2}}} is not an integer. Moreover, 1 {\displaystyle 1} and 2 {\displaystyle {\sqrt {2}}} do not have an integer common multiple because 2 {\displaystyle {\sqrt {2}}} is irrational. Pythagorean triples have been known since ancient times. The oldest known record comes from Plimpton 322, a Babylonian clay tablet from about 1800 BC, written in a sexagesimal number system. It was discovered by Edgar James Banks shortly after 1900, and sold to George Arthur Plimpton in 1922, for $10.When searching for integer solutions, the equation a2 + b2 = c2 is a Diophantine equation. Thus Pythagorean triples are among the oldest known solutions of a nonlinear Diophantine equation.

WikidataRate this definition:4.2 / 6 votes

1. 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, 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 coprime. A right triangle whose sides form a Pythagorean triple is called a Pythagorean triangle. The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula a² + b² = c²; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples. For instance, the triangle with sides a = b = 1 and c = √2 is right, but is not a Pythagorean triple because √2 is not an integer. Moreover, 1 and √2 do not have an integer common multiple because √2 is irrational.

Editors ContributionRate this definition:0.0 / 0 votes

1. pythagorean triple

   Pythagorean triple is a set of three whole numbers which represent the lengths of the sides of a right angle triangle.

   Multiples of Pythagorean triples can be formed by multiplying a given set by a whole number. Eg (3,4,5) = 2×(3,4,5)= (6,8,10)

   
   

   Submitted by anonymous on October 17, 2020  

How to pronounce Pythagorean triple?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

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   Indian

   Priya

   Indian

   Neerja

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   Zira

   US English

   Oliver

   British

   Wendy

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   Fred

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   Tessa

   South African

How to say Pythagorean triple in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of Pythagorean triple in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of Pythagorean triple in Pythagorean Numerology is: 3

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Pythagorean_Triple
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Pythagorean_Triple
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=Pythagorean triple