Pythagorean Triangle/Examples/693-1924-2045

Example of Primitive Pythagorean Triangle

The triangle whose sides are of length $693$, $1924$ and $2045$ is a primitive Pythagorean triangle.



Proof

\(\ds 693^2 + 1924^2\) \(=\) \(\ds 480 \, 249 + 3 \, 701 \, 776\)
\(\ds \) \(=\) \(\ds 4 \, 182 \, 025\)
\(\ds \) \(=\) \(\ds 2045^2\)

It follows by Pythagoras's Theorem that $693$, $1924$ and $2045$ form a Pythagorean triple.


Note that $693$ and $1924$ are coprime.

Hence, by definition, $693$, $1924$ and $2045$ form a primitive Pythagorean triple.

The result follows by definition of a primitive Pythagorean triangle.

$\blacksquare$


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $13$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $13$
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.