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What Might Have Been

December 14, 2016

If a triangle has a right angle, and if the two shorter sides are 3 and 4 units long, then the longest side must equal 5 units.  That’s because 32 + 42 = 52.  Although this is not the Pythagorean Theorem per se, it is perhaps the most common demonstration of its practicality.  However, this demonstration is not a proof.  It merely shows one case.  A proof shows how the same conditions will give the same result in each and every case, and that is exactly what Congressman James Garfield did in the 1870s.

He was not the first to offer a proof of the Pythagorean Theorem.  Scores of mathematicians over more than two millennia had preceded him.  Garfield, however, was the first to show how the   axioms which pertain to trapezoids can be used to prove the theorem.  Garfield did not discover this proof in order to affect legislation.  It was just something he did in his spare time.

In the 21st century, when Federal spending has been out of control for decades, it may seem odd that there was once a Congressman who could actually do math, but there is a better reason to notice Garfield’s accomplishment.  We have all heard of Jefferson’s brilliance.  Those who know history are informed regarding the intellect of John Quincy Adams.  There are many who still remember the Kennedy wit and the cagey intelligence of Ronald Reagan.  But no one will ever know what might have been accomplished if the hard working and intelligent James Garfield had lived to serve out the remaining three and a half years of his presidential term.

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