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Topic: [HM] "President Garfield's Proof"
Replies: 20   Last Post: Feb 29, 2000 8:46 PM

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Clark Kimberling

Posts: 20
Registered: 12/3/04
[HM] "President Garfield's Proof"
Posted: Jan 14, 2000 10:38 AM
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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 12-line 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





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