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?
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.
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.
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