The Pythagorean relation ABSOLUTELY holds for a triangle whose legs are both 1 and whose hypotenuse is 2^(1/2). Pythagoras’ cult simply didn’t believe in irrational numbers, hence their trouble when the Pythagorean relation implied it. It is known there was even a proof at the time of the irrationality of the square root of two.
More specifically, I don’t know how advanced the details of mathematical philosphy were at the time. But a discussion point might be that just because irrational numbers are logically possible, doesn’t mean they’re “real” (in some sense). However, being constructible using basic geometric arguments (as a right angled isolese triangle is) would make arguing against their existence much more difficult.
The Pythagorean relation ABSOLUTELY holds for a triangle whose legs are both 1 and whose hypotenuse is 2^(1/2). Pythagoras’ cult simply didn’t believe in irrational numbers, hence their trouble when the Pythagorean relation implied it. It is known there was even a proof at the time of the irrationality of the square root of two.
More specifically, I don’t know how advanced the details of mathematical philosphy were at the time. But a discussion point might be that just because irrational numbers are logically possible, doesn’t mean they’re “real” (in some sense). However, being constructible using basic geometric arguments (as a right angled isolese triangle is) would make arguing against their existence much more difficult.