From charlesreid1

Problem 9 on Project Euler:

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.