1e+-+James+A.+Garfield+(1876)

How many presidents dabbled in mathematics? Quite a few, actually. Abraham Lincoln even "carried a copy of Euclid's Elements with him and studied it at night by candlelight ( Berlinghoff & Gouvea, 2004, p. 158)." Why? Well, to become a better lawyer, of course. Lincoln believed that the logic and structure of mathematics would serve him in other areas. But James Garfield is the only president to ever publish a proof of the Pythagorean Theorem. Like Perigal, Garfield was an amateur. He was also self schooled having written in his diary in October 1851, "I have today commenced the study of geometry alone without class or teacher (Posamentier, 200, p. 174)." Like Lincoln, he found math stimulating, once noting that "his mind was 'unusually clear and vigorous' when studying mathematics ( Berlinghoff & Gouvea, 2004, p. 142)." media type="custom" key="6211179" Created using GeoGebra 3.2.40.0 GeoGebra - Dynamic Mathematics for Everyone []

The green and blue triangles are congruent right triangles. They are aligned such that points C, E, and B are collinear.

1. Quadrilateral ABCD is a trapezoid. Does this suggest a proof to you?

2. Express the area of the trapezoid in terms of a and b.

3. Express the area of all three triangles in terms of a and b. If you have trouble with the white triangle, check on the "Show Hint" checkbox. Can you prove the hint?

4.Relate the area of the trapezoid to the area of the triangles. Express this relationship using only the variables a, b, and c.

5. Does this prove the Pythagorean Theorem?

6. Slide the "Rotation" slider from left to right. Did the result surprise you? Why or why not?