Cool Proofs

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When I first saw a geometric proof of the Pythagorean theorem several years ago, I wondered why they didn't present this in my geometry class way back then when I took it in 9th grade. Here is the straightforward proof: mathforum.org and here is an interesting geometric proof that isn't as straightforward but can be followed nonetheless sunsite.ubc.ca

Anybody else have other interesting proof examples to share?

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I agree, in math having a deep understanding is what makes the subject enjoyable. Whoever has done very well in math and really gets it without having to rely on rote memorization is very fortunate, especially when seeing how others get progressively worse off as they keep memorizing and not understanding math. Going through proofs is one way to solidify understanding and add insight, and definitely gives you an edge in solving more challenging problems.

Often the most simplest proof is the most elegant proof.
Simply put beauty is simplicity in mathematics and beyond.

Thanks, I'm glad you liked it, and this math forum post has links to many more ways to prove the Pythagorean theorem: mathforum.org - I personally like the simplest and most elegant proofs, though others may prefer the most convoluted and unexpected approaches to yield a solution.

very enjoyable. Thanks for posting!

Kudus for Omar... yes that was it :)

I'm from Egypt too but I grew up in the US, and in the public schools I went to they underestimated our minds the most when we were younger then it got better by the time I reached high school :) How I would do it is have the chord drawn with one end touching one end of the diameter. By definition of a diameter you can mark a centerpoint of the diameter and divide it into two radial lines. Now you just draw a line from that centerpoint to where the other end of the chord is. This creates an isosceles triangle (sides r, r, and chord length). Is it an axiom that the sum of two sides of a triangle is always greater than the third side? If so then r + r > chord hence d > chord.

Here is another cool proof that we took in 8th grade. Egypt is not that bad ;) but the more we grow up the more they underestimate our mind :)

Proof that the length of the diameter of a circle is greater than that of any other chord in it?

Hint: you could proof it in many ways, but how can you do that in 2-3 lines with 8th grade's knowledge (no sin nor cosin nor even right triangles:)?

you know what? we took it as an axiom (mosalamah in arabic) when I was in 9th grade at Egypt:).

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Cool Proofs

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Village Journals

Resonate your identity with Naseeb journals. Express your opinions, share your thoughts, post your writings and connect with like minded people through the power of expression.