# Pythagorean triples? 3-4-5, and 5-12-13

• Dec 17th 2012, 10:25 PM
asilvester635
Pythagorean triples? 3-4-5, and 5-12-13
can anyone explain this concept to me?
• Dec 17th 2012, 10:29 PM
jakncoke
Re: Pythagorean triples? 3-4-5, and 5-12-13
Basically, a pythogorean triple is just 3 positive integers which satisfy the pythogorean theorem $\displaystyle a^2 + b^2 = c^2$.
So $\displaystyle 3^2 + 4^2 = 5^2 \text{ and } 5^2 + 12^2 = 13^2$
• Dec 17th 2012, 10:35 PM
MarkFL
Re: Pythagorean triples? 3-4-5, and 5-12-13
In a nutshell, a Pythagorean triple $\displaystyle (a,b,c)$ has the property that $\displaystyle a^2+b^2=c^2$

Perhaps the best know method for generating such triples (attributed to Euclid) is to let:

$\displaystyle a=m^2-n^2$

$\displaystyle b=2mn$

$\displaystyle c=m^2+n^2$

where $\displaystyle n<m$ and $\displaystyle m,n\in\mathbb{N}$.

A triple is said to be primitive if $\displaystyle a,b,c$ are co-prime, and requires $\displaystyle m,n$ to be co-prime and $\displaystyle m-n$ is odd.

Pythagorean triple - Wikipedia, the free encyclopedia