Definition:Pythagorean Triple
Jump to navigation
Jump to search
Definition
A Pythagorean triple is an ordered triple of positive integers $\tuple {x, y, z}$ such that $x^2 + y^2 = z^2$.
That is, a Pythagorean triple is a solution to the Pythagorean equation.
Primitive Pythagorean Triple
Let $\tuple {x, y, z}$ be a Pythagorean triple such that $x \perp y$ (that is, $x$ and $y$ are coprime).
Then $\tuple {x, y, z}$ is a primitive Pythagorean triple.
Also known as
A Pythagorean triple is also known as a (set of) Pythagorean numbers.
Also see
- Pythagoras's Theorem
- Definition:Pythagorean Triangle
- Definition:Pythagorean Equation
- Solutions of Pythagorean Equation
- Results about Pythagorean triples can be found here.
Source of Name
This entry was named for Pythagoras of Samos.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Pythagorean triple or Pythagorean numbers
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.9$: Hypatia (A.D. $\text {370?}$ – $\text {415}$): Appendix: A Proof of Diophantus' Theorem on Pythagorean Triples
- 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Pythagorean Triples
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Pythagorean triple
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $7$: Patterns in Numbers: Diophantus
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Pythagorean triple