
[HM] "President Garfield's Proof"
Posted:
Jan 14, 2000 10:38 AM


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. Occupying roughly 1/3 page, the piece starts as follows:
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ PONS ASINORUM
[In a personal interview with Gen. James A. Garfield, Member of Congress from Ohio, we were shown the following demonstration of the pons asinorum, which he had hit upon in some mathematical amusements and discussions with other M. C.'s. We do not remember to have seen it before, and we think it something on which the members of both houses can unite without distinction of party.] ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
That introduction is followed by a figure and 12line proof.
(Note that "pons asinorum" refers to the Pythagorean theorem, rather than the fifth proposition of the first book of Euclid. Both references have been noted elsewhere.)
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."
Clark Kimberling

