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e^(i*pi) = -1

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e^(i*pi) = -1

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You can argue, this is the most important formula in all of science and engineering.

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You can argue, this is the most important formula in all of science and engineering.

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I always thought that honor belonged to the formula for beer...

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Zounds, I had forgot the beer.

-drl

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Demonstration of the Pythagorean Theorem using squares (actual squares)

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Can we prove (or disprove) similar for, say, cubes?

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The Golden Ratio:
a+b/a = a/b = 1.618033988...
and its reciprocal b/a = 0.618033988...

I used it quite a bit back in my cabinet-making days.

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Yup - calculated the most visually pleasing length of dew shield for my atm refractor with this ratio...

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The Golden Ratio:
a+b/a = a/b = 1.618033988...
and its reciprocal b/a = 0.618033988...

I used it quite a bit back in my cabinet-making days.

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Demonstration of the Pythagorean Theorem using squares (actual squares)

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Can we prove (or disprove) similar for, say, cubes?

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Fermat's Conjecture (Fermat's Last Theorem)

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Demonstration of the Pythagorean Theorem using squares (actual squares)

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Can we prove (or disprove) similar for, say, cubes?

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Fermat's Conjecture (Fermat's Last Theorem)

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Correct, and I think a few of you picked up on my sly (if inaccurate) attempt at mathematical humour

Cubes do not add up in the way squares do. There was an old proof for cubes, over a century old I think...

There was an older (unproved) assertion that in fact, it doesn't add up for all exponents bigger than squares. My understanding is it's this Fermat reckoned he'd proved.

So Otto's suggestion of Pythagoras' theorem is another one of those ideas that has a lot more to it than at first appears...

Edited by Ravenous (01/07/13 06:58 AM)

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I am curious, is the pythagorean theorem or some version of it applicable to spherical trig (triangles on the surfaces of spheres and other shapes)?

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If a Möbius strip is going to be included, shouldn't a Klein bottle be too?

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'Topology' is about mapping one shape onto another(and hopefully back), same applies to the triangle onto sphere, any shape onto another, there's more than one way around the barn though I think the branches (algebraic or point set) are converging (if not considered already so). Relatively simple questions like this can be astonishingly difficult to prove - as was the recently solved Poincare Conjecture. It's important to consider exactly which space(flat, curved, other) you are mapping to and from and backwards upside down. It's in many ways important to consider if asking for all potential sizes or small from one to another. Small triangle onto large Klein bottle, Moebius stip, sphere... or large onto small... helps if creating a Klein bottle 'opener'

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