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Garfield's Proof of the Pythagorean Theorem

This Demonstration shows President James Garfield's elegant proof of the Pythagorean theorem.
The area of the trapezoid (step 5) can be calculated in two ways: as a trapezoid with base and heights and , or as the sum of the areas of three triangles:
.
Multiply through by 2 and expand the left-hand side to get
,
which simplifies to
.

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James Abram Garfield (1831–1881), the twentieth president of the United States, published this proof in the New England Journal of Education.
Reference
[1] S. Klebe, "Garfield, the Pythagorean Theorem, and the Fight for Universal Education," Executive Intelligence Review, 22(9), 1995 pp. 50–51. www.larouchepub.com/eiw/public/1995/eirv22n09-19950224/eirv22n09-19950224_050-garfield_the_pythagorean_theorem.pdf.
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