Garfield's Proof of the Pythagorean Theorem

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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



Contributed by: Alvaro José Ibarra Rivas (March 2013)
Open content licensed under CC BY-NC-SA



James Abram Garfield (1831–1881), the twentieth president of the United States, published this proof in the New England Journal of Education.


[1] S. Klebe, "Garfield, the Pythagorean Theorem, and the Fight for Universal Education," Executive Intelligence Review, 22(9), 1995 pp. 50–51.

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