Wolfram Demonstrations Project

13,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Garfield's Proof of the Pythagorean Theorem

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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

[more]

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

.

[less]

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

Snapshots

Details

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.

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send