A US President’s Proof of the Pythagorean Theorem

James Garfield, the 20th president of the United States, came up with an original proof of the Pythagorean Theorem in 1876 when he was still a Congressman. His proof was published in New England Journal of Education.

Pythagorean Theorem proof by President Garfield

Recall that the Pythagorean Theorem states that given a right triangle with sides a, b, and hypotenuse c, the following equation is always satisified:

a^2 + b^2 = c^2.

President Garfield’s proof is quite simple. We can do this in three steps:

  1. Find the area of figure above using the trapezoid
  2. Find the area of the same figure using the three triangles
  3. Equate the results in 1 and 2. » Read more
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