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- Thread starter eprjenkins
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In summary, the conversation discusses various proofs of the Pythagorean theorem, including a one-word proof and one by Euclid. The conversation also mentions a proof by American president James Garfield and how to think about the theorem. The conversation ends with a comment about the difficulty of creating one's own proofs.

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http://www.aurora.edu/mathematics/bhaskara.htm

here is the proof by euclid:

http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI47.html

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Thankyou all very much.

Just been reading some of them. Bhaskara's proof is excellent.

Just been reading some of them. Bhaskara's proof is excellent.

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HallsofIvy said:

actually, it was mckinley's assassination that gave us Teddy's first term of office. Chester Arthur was Garfield's successor.

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now change the angle of the lines subdividing the square, until they leave a small square in the center, with 4 right triangles around it of sides a,b,c.

then the small square in the center has area (b-a)^2, and the 4 triangles have total area 2ab, so the sum of 2ab and (b-a)^2 must equal c^2.

QED.

i found this proof sitting on the plane for a while with a small scrap of paper, (and not playing with a calculator).

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apparently i rediscovered bhaskara's proof, but my remark on the special case shows you how to think of it, which he does not.

notice the reason I am able to tell you how to think of it, is that i did think of it myself, and did not just read it and memorize it.

notice also that my example illustartes a basic principle in problem solving: i.,e. MAKE THE PROBLEM EASIER. then solve the easier problem and try again to use what you learned on the harder one.

notice the reason I am able to tell you how to think of it, is that i did think of it myself, and did not just read it and memorize it.

notice also that my example illustartes a basic principle in problem solving: i.,e. MAKE THE PROBLEM EASIER. then solve the easier problem and try again to use what you learned on the harder one.

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The day i can make my own proofs i will be very happy.

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Doodle Bob said:actually, it was mckinley's assassination that gave us Teddy's first term of office. Chester Arthur was Garfield's successor.

I knew that! Apparently I'm better at math than I am at history!

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