as far as the rationals are concerned, this is the same as the number whose square is 2. (ℚ(i) and ℚ(√2) are isomorphic as fields.)
what we can gleam from this is that complete rationality can blur the line between what’s real and what’s imaginary
But Pythagoras hated triangles with irrational hypotenuses. A triangle with leg lengths of 3 and 4 units? Beautiful. A triangle with two 1 unit legs? Die
And not a right triangle in sight. I forget, did Pythagoras develop Pythagorean theorem or the law of sines?
Well, he popularized it, but the Pythagoran theorem was something ancient civilizations had already figured out.
It's really just whose discovery spread the fastest. There have been a few instances in history where parallel discoveries happened, but it got named after the guy who got it popularized fastest.
Plus, the records of the civilization that discovered it were lost for a few millenia. But it's not the first thing that's been rediscovered a few times.
Unless the "documenter" wasn't a real person.
The Pythogean Cult is very fun reading.
