# Definition:Pythagorean Triangle/Historical Note

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## Historical Note on Pythagorean Triangle

**Pythagorean triangles** were known to the ancient Babylonians in about $2000$ BCE.

The cuneiform tablet *Plimpton $\mathit { 322 }$* list $15$ sets of Pythagorean triples.

It is also clear that the author of that tablet was also familiar with the fact, proved in Solutions of Pythagorean Equation, that the numbers $2 p q$, $p^2 - q^2$ and $p^2 + q^2$ always make a Pythagorean triangle.

It is likely that the ancient Greeks, and in particular Pythagoras or one of his disciples, obtained this result from the Babylonians.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $13$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $13$