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Suppose I wanted to find out about the Pythagorean Theorem by searching via WolframAlpha. This is trivial -- we can search directly for Pythagorean Theorem and get a wealth of information.

But suppose instead that I wanted to find that same information without knowledge of the theorem's name. Suppose I only knew that a^2 + b^2 = c^2 for a right triangle with legs a and b and hypotenuse c. Searching purely by that formula doesn't yield the desired result -- and indeed it shouldn't, as we left out some important details!

I am curious if other cases exist where you can do this on WolframAlpha. Are there any such queries where we can input colloquial formulas, and return an association with some related theorem?

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Good question. Seems to be a problem with WolframAlpha itself to not see the link between the equation and the theorem name. Google however doesn't fail me. –  Hydra Feb 12 '13 at 3:10
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