# Pythagorean Theorem: Proving it with Maths

• eprjenkins
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.

#### eprjenkins

I have used the pythagorean theorem quite frequently yet have never have it proved for me. I tried to do so myself but as i suck at maths i was unsuccessful. Any links proving it would be apppreciated.

Note that the fifth proof was due to American president James Garfield. Probably the only thing he did of any importance! (Other than getting assassinated and making Theodore Roosevelt president.)

Thankyou all very much.

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HallsofIvy said:
Note that the fifth proof was due to American president James Garfield. Probably the only thing he did of any importance! (Other than getting assassinated and making Theodore Roosevelt president.)

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

subdivide a square of side c, into 4 equal parts by the two diagonals. note this gives a simple case of the theorem, when a=b, since the area of the square is c^2 and the areas of the 4 triangles is 2 a^2. i.e. a^2 + a^2 = c^2.

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).

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.

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

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!