President Garfield and the Pythagorean Theorem

Date: 7 Mar 1995 14:27:08 -0500
From: "Geraldine A. Chase"
Subject: Pythagorean Theorem

Dear Dr. Math,

My first year algebra class is studying the Pythagorean Theorem 
at this time.  I know that one proof of the Pythagorean Theorem 
was done by James Garfield, before he became President of the 
United States.  Can you give me any more information?  What year?  
Where is it published, etc.

Date: 7 Mar 1995 14:27:08 -0500
From: Annie Fetter
Subject: Re: Pythagorean Theorem

Hi Geraldine.  This got passed on to me as supposed resident geometer.
James Garfield discovered a proof of the Pythagorean Theorem in 1876, 
which was indeed a few years before he became President.  It's based 
on the trapezoid, and is related to the proof that many people are 
familiar with the square within a square.  I'm not sure where it was 
originally published - I got my information from a new book called 
Pythagoras Plugged In, which is just being released by Key Curriculum 
Press (it's a companion book to the Geometer's Sketchpad materials).  
If you'd like more information about the proof, just let me know.  (As 
a hint as to how you might investigate his proof, draw the standard 
square-within-a-square picture.  Now draw a diagonal of the inner 
square, and remove "half" of the drawing.  Now you've got what he 
ended up with in his proof, though he constructed it another way.)

        -Annie, Consulting Physician