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From Don Jewett, University of California

Ian Stewart’s article on elegant mathematical proofs (“Proof and beauty”, 26
June, p 28) reminds me of a proof in plane geometry whose elegance most will
comprehend.

Given an isosceles triangle ABC (A being the vertex), where side AB = side
AC, prove that angle C = angle B. (The usual proof involves bisecting angle A
and proving that the two smaller triangles are identical.)

Proof: Note two triangles: ABC and ACB. Since AB = AC and angle A is the same
in both, then the two triangles are identical, based upon equality of
side-angle-side. Hence angle B = angle C.

The interesting thing about this aesthetically appealing proof is that it was
generated by a computer. So beauty, even in mathematics, is in the eye of the
beholder, rather than the intent of the solver.

San Francisco