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
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.
New “John Lennon beat his wife” guy just dropped.
John Lennon stopped beating his wife when the imaginary numbers patch dropped for Pythagorean Theorem™
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
3 days late but i would like to recognize that i am wrong