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Thread: Pythagorean triples? 3-4-5, and 5-12-13

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

    can anyone explain this concept to me?
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    Senior Member jakncoke's Avatar
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    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 $
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    MHF Contributor MarkFL's Avatar
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    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
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