WOLFRAM|DEMONSTRATIONS PROJECT

Garfield's Proof of the Pythagorean Theorem

measure of angle ABC

0.5

step

1

2

3

4

5

This Demonstration shows President James Garfield's elegant proof of the Pythagorean theorem.

The area of the trapezoid

CADE

(step 5) can be calculated in two ways: as a trapezoid with base

a+b

and heights

a

and

b

, or as the sum of the areas of three triangles:

(a+b)(a+b)/2=

2

c

/2+2ab/2

.

Multiply through by 2 and expand the left-hand side to get

2

a

+2ab+

2

b

=

2

c

+2ab

,

which simplifies to

2

a

+

2

b

=

2

c

.