Pythagorean Triple/Examples/8, 15, 17
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Example of Pythagorean Triple
The triple $\tuple {8, 15, 17}$ forms a Pythagorean triple which is also a primitive Pythagorean triple.
Proof
| \(\ds 8^2 + 15^2\) | \(=\) | \(\ds 64 + 225\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 289\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 17^2\) |
Hence $\tuple {8, 15, 17}$ is a Pythagorean triple by definition.
We also have that $8 \perp 15$, demonstrating that $\tuple {8, 15, 17}$ is a primitive Pythagorean triple.
$\blacksquare$
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Pythagorean triple