Subject: Re: [HM] "President Garfield's Proof"
From: Julio Gonzalez Cabillon (jgc@adinet.com.uy)
Date: Sun Jan 23 2000 - 11:48:24 EST
[Clark Kimberling]
:
: A number of printed sources contain, under the heading "President
: Garfield's Proof" (or some variant) an attractive proof of the
: Pythagorean theorem. The attribution to James Arthur Garfield seems
: to be widely accepted.
:
: An early reference is The Journal of Education 3 (1876) 161.
: ...
:
: A Garfield biographer responded to my inquiry that he has never
: encountered any direct support for "Garfield's Proof", and
: "... considering that G never mentions the proof or even shows much
: interest in geometry in his voluminous boyhood letters and diaries,
: I have my doubts."
[JGC's forward of a Librarian at WC]
|
| James A. Garfield studied Greek and Mathematics at Williams College.
| He did indeed provide a proof of the Pythagorean Theorem. He referred
| to it as Pons Asinorum. His proof was first published in The Journal
| of Education 3:161, in 1876. In a journal entry dated March 7, 1876,
| Garfield states that during a visit to Keene, VT he showed his proof
| to Professor Quimby who was Professor of Mathematics at Dartmouth Univ.
| ...
[Clark Kimberling]
: ...
:
: Here is what Professor Peskin wrote about the 1876 journal entry:
:
: "Of course the Garfield diary for 1876 mentions the proof, but my
: concern was whether Garfield had devised it as A SCHOOLBOY, as the
: story sometimes has it. And, in that context, I have found no
: evidence of any particular interest in geometry in general or that
: proof in particular that stemmed from his early years. I may have
: overlooked something, but if so, so did Hendrick Booraem in his
: otherwise exhaustive study of Garfield's adolescence, THE ROAD TO
: RESPECTABILITY. In the absence of any such evidence, I decided to
: omit the tale from my biography. If you find anything that I
: overlooked, please let me know."
1* If there is a journal entry dated March 7, 1876, where Garfield
states that during a visit to Keene, VT he showed his proof to Professor
Quimby [Professor of Mathematics at Dartmouth University] I would not
say that "I have never encountered any direct support for _Garfield's
Proof_".
2* The issue that "Garfield never mentions the proof in his voluminous
BOYHOOD letters and diaries" does not contradict 1*.
3* Since Garfield was born in 1831, the entry "dated March 7, 1876" does
not establish (a priori) any link with Garfield's adolescence. So the
concern as to whether "Garfield had devised it as A SCHOOLBOY, as the
story sometimes has it" seems to be (at least to me) far-fetched. If,
in fact, Garfield had devised his proof as a SCHOOLBOY, my first reaction
(concern?) would be why he took so long to make it known ...
Julio Gonzalez Cabillon
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