Hi Ganesh;

How are you?

Hi Agnishom,

Fine, Thanks.

Regarding your query, you may PM bob bundy, and zetafunc. They may help you.

Good wishes.

]]>How are you?

My concern is that I am not sure what the pythagorean theorem is saying in terms of modern mathematics? For example, is it a statement about metric spaces? Well, if we are talking about R^2 with the l_2 norm, then the statement is trivial, if we are not talking about this particular metric on R^2, then the "theorem" seems to be false.

Is it then telling us that l_2 norm is the God-given norm for R^2? What does that mean?

I think the correct answer is that the pythagorean theorem somehow tells something about inner-product spaces. But I still don't get what it is.

]]>where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides. The theorem, whose history is the subject of much debate, is named for the ancient Greek thinker Pythagoras.

The theorem has been given numerous proofs – possibly the most for any mathematical theorem. They are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and indeed, to objects that are not triangles at all, but n-dimensional solids. The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power; popular references in literature, plays, musicals, songs, stamps and cartoons abound.

For details, see the link Pythagoras' Theorem.

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