Today is the day we observe Washington’s Birthday, popularly known as Presidents’ Day, and that makes it a good day to look at the Pythagorean Theorem. Specifically, a proof of the Pythagorean Theorem. Specifically, the proof created by James A. Garfield, the 20th president of the United States.

The Pythagorean Theorem, often written as , says that squares on the legs of a right triangle, added together, have the same area as a square on the hypotenuse, Garfield’s proof, published 5 years before he assumed the presidency, used a trapezoid. Here’s a photo from the New-England Journal of Education on April 1, 1876

Garfield’s proof compares the area of the trapezoid (the height times the average of the parallel sides) with the area of the three triangles that make up the trapezoid. Garfield wrote out the details for you above, but feel free to try it using the common ab and c notation.

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