Yeah, I saw the Donald Duck
thing, too. I think I saw it as a double, with that story about the goofy lady that loses her bracelet in the donut dough...
Anyway, yeah, Pythagoras was religious, sort of. He had all sorts of crazy, radical ideas like;
All his contemporaries (like Heraclitus, Xeno, or Anaxamender) were arguing whether the prime substance of Reality was fire, air, water, earth, or aether. Since quantum mechanics can only be understood with math, I'd say he was pretty sharp, despite (or maybe because of) his spiritualism.
The reason his cult used the pentagram, is because whichever segments you compare, the ratio of their lengths are some power of the golden ratio:
1.618n , where n is 1, 2, or 3.
(I know, because after I saw the Disney video, which mentions the fact, I proved it to myself - the pentagram, and the fingers.)
They put it on their hands, since the same ratio is expressed in the segments of your fingers
For those that missed the video, the golden ratio can be calculated by taking the Fibonacci series (1,1,2,3,5,8,13,24,31..) out several values, then taking the ratio of any pair...it approaches 1.618 = 1/.618 That's why it's golden - if you take away a square, you still get the same ratio.
What's weird is that the spirals found in nature often adhere to not only the ratio, but the series, even in the low numbers. Pinecones have little nubs on them, and if you look down on it, there's 5 rows making one spiral, or 8 rows going the other way. Sunflowers have 24 and 31...
Pythagoras is also credited with recognizing why certain sounds work well together - the whole number fractions between the 'tuned' notes. He considered string length. We now 'know' that it's the frequency - because the prime substance of the Universe is number.
I guess you'd only care about that kind of thing if you haven't been traumatized by algebra propaganda.
Well, rumor has it that the Egyptians, or possibly even the Thais, invented the actual theorem first, so blame them.
Pythagoras was probably just the first guy to hear of it in the local region, recognize it's value, and write it down, as part of the proof for his 'pet' theory.