how did pythagoras come up with the pythagoren theorem?

Question

a day in the life of pythagoras; the day when he came up with the pythagorean theorem

Answer 1

First, there is some question whether a real Pythagoras ever existed. Maybe he did, though; there was something called the "Pythagorean School" in ancient Greece where all the followers thought that everything in the world is governed by numbers ... sort of like horoscopes today.

The next thing about this famous theorem is that there are zillions of proofs of it (well, maybe 400). President James Garfield came up with one himself, and so did I. (Well, I'm sure others have done the same thing; I just never saw it quite the way I did it.)

The third thing is the way the Greeks, including Pythagoras, I'm sure, thought about it. We learn it as a^2 + b^2 = c^2, or maybe the square of the hypoteneuse equals the sum of the squares of the legs.

But we're thinking of it algebraically. The Greeks didn't have algebra the way we think of it. Instead, they used what we might call "geometric algebra" which seems a bit strange unless you're used to it.

Anyway, to keep a long story long, the Greeks would say "the square the hypoteneuse equals the sum of the squares the sides." What they'd do is draw a right triangle, then make squares stick out from each of the three sides. It looked like a windmill.

Since we don't know for sure that Pythagoras really existed, we don't know for sure that he ever proved his theorem. In any event, the most famous proof by far is the one provided by Euclid, another Greek, who lived 200 years after Pythagoras (300 BCE). Euclid's proof uses the windmill set-up and is called the "windmill proof". Maybe this is the same one Pythagoras himself used; we don't know. But Euclid's geometry text was used for the next 2300 years, almost right up to the present day.

And that's all I can tell you about Pythagoras.

Answer 2

I was told one day Pythagoras was playing with wooden blocks or cubes and he noticed that the sum of the square areas of the two sides of the triangle that make the right angle equaled the value of the square of the remaining side.

Answer 3

These two sites should suffice:

http://www.geom.uiuc.edu/~demo5337/Group3/hist.html

http://en.wikipedia.org/wiki/Pythagorean_theorem