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In article <1992Apr9.090734.1@scivax.stsci.edu> reinhard@scivax.stsci.edu writes:
>
>Can any one tell me which U.S. President developed a proof to the 
>Pythagorean Theorem?
James Abram Garfield.  He was the one that Garfield High School is named
after.  Of course, the town where I grew up had TWO high schools --
I went to Garfield's cross-town rival, Charles Guiteau High School.

Garfield found a proof of the Pythagorean Theorem.  Of course, this was
before he was President.  The story says that he found the proof
when he was a member of the House of Representatives,
while doodling one day during a boring speech...

The proof, known in the literature of the Pythagorean theorem as
"General Garfield's Demonstration", was reprinted in the Mathematical
Magazine, volume I, no. 1, page 7 (January 1882).

It was published originally in a magazine article, in 1876 or 1877,
but that reference is apparently unknown:  a copy of it was pasted
in the flyleaf of somebody's old geometry book, and so Garfield's
proof is known today only because of that copy.

--
  Gerald A. Edgar                Internet:  edgar@mps.ohio-state.edu
  Department of Mathematics      Bitnet:    EDGAR@OHSTPY
  The Ohio State University      telephone: 614-292-0395 (Office)
  Columbus, OH 43210             -292-4975 (Math. Dept.) -292-1479 (Dept. Fax)

   It was James A. Garfield. His proof was different from the
   preceeding proofs. I do not remember in what manner. The
   Pythagorean Theorem has hundreds of different proofs.
 
 
 
                        Silence is better than unmeaning words.
                                     - Pythagoras (6th C. b.c.)

In article <1992Apr9.153901.5109@newshost.lanl.gov> ttw@beta.lanl.gov (Tony Warnock) writes:

>   It was James A. Garfield. His proof was different from the
>   preceeding proofs. I do not remember in what manner. The
>   Pythagorean Theorem has hundreds of different proofs.

His proof is essentially using half of the figure of Bhaskara's (sp?) proof,
although it is quite possible he did not know that proof.  The figure is that
of a trapezoid with vertical left side, and right angles at the left corners.
If the triangle has sides a and b, and hypotenuse c, the figure has horizontal
lengths of a and b, vertical a+b, and one equates the area of the trapezoid
with the sum of two copies of the original triangle and an isosceles right
triangle with side c.
-- 
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: (317)494-6054
hrubin@pop.stat.purdue.edu (Internet, bitnet)  
{purdue,pur-ee}!pop.stat!hrubin(UUCP)