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Old 2021-10-15, 06:36   #1
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"Matthew Anderson"
Dec 2010
Oregon, USA

3×17×19 Posts
Default a proof without words of good 'ol pythagorean theorem

Hi all,

So I placed high in a few math contests back in the 1990's. I even won two medals for it. They had a nice picture on them. Thank goodness for my wife, who puts up with me. So books about proofs without words are available from the Mathematica Association of America. I am a lifetime member of this Association.

A non-sponsored plug for a Amazon book.


Fill in the algebra, if you can.

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Old 2021-10-15, 13:12   #2
Dr Sardonicus
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Feb 2017

120218 Posts

See The Many Proofs of the Pythagorean Theorem.

The diagram in the OP is from Bhaskara's first proof ("Behold!"), which dates to the Twelfth Century.

The earliest known proof is in the Chou Pei Suan Ching and is much older. It uses the hsuan-thu diagram, a square of side a + b. Each corner includes the right angle of a right triangle with legs a and b. The square is thus divided into four (congruent) right triangles with legs a and b, and an inner square with side equal to c, the hypotenuse.

The segment between the points dividing the top and bottom sides in the hsuan-thu diagram divides the square into two congruent trapezoids with altitude a+b, and bases a and b.

As described here, in 1876 James Garfield (then U.S. representative of the 19th District of Ohio), devised a proof of the Pythagorean Theorem by computing the area of the trapezoid in two different ways. It was published in The New England Journal of Education.
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