Legs of Pythagorean Triangle used as Generator for another Pythagorean Triangle/Examples/3-4-5
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Example of Legs of Pythagorean Triangle used as Generator for another Pythagorean Triangle
The $3-4-5$ triangle has hypotenuse $5$.
By Solutions of Pythagorean Equation, the Pythagorean triangle $P_2$ formed by the generator $\tuple {4, 3}$ is:
| \(\ds P_2\) | \(=\) | \(\ds \tuple {2 \times 4 \times 3, 4^2 - 3^2, 4^2 + 3^2}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \tuple {24, 7, 25}\) |
It is observed that $25 = 5^2$.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $13$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $13$