Pythagorean Triples

[eastlondoner]

In any set of Pythagorean triples a b c which are positive integers such that a squared plus b squared equals c squared (e.g. 3 4 5 or 5 12 13) is it always true that a + b > c, a + c > b, and b + c > a?

[jim360]

Yes, although that's not because the numbers form Pythagorean triples. Instead, it's because they are sides of a triangle. The lengths of any two sides of a triangle must be greater than the length of the third side -- which is another way of saying that "the shortest distance between two points is a straight line between them", as opposed to any other journey.

[eastlondoner]

Thanks jim360, I should have thought of that.

[jim360]

You're welcome. But don't beat yourself up too much about missing the obvious, it happens to everybody!