Project Euler/9

Problem 9 on Project Euler: https://projecteuler.net/problem=9

In this problem, you are asked to find three Pythagorean triples with a specified sum.

This is equivalent to solving a quadratic equation (the Pythagorean theorem) and a linear equation (sum of three variables is a constant).

$a+b+c-1000=0$

$a^{2}+b^{2}-c^{2}=0$

This can be visualized as the intersection of a plane and a cone.