Bringing up the fact that Pythagorean theorem doesn’t work when one of the known values is √2. Pythagoras really didn’t like this
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.
Pythagorean theorem works, I think you might be confusing this with the fact that the Pythagoreans rejected the notion of irrational numbers, but √2 is the length of the hypotoneuse of a right angle triangle where the other sides are unit length
