[FOM] The Steiner-Lehmus theorem
silver_1 at mindspring.com
Sat Aug 20 11:02:43 EDT 2011
The "innocent" Steiner-Lehmus theorem has stumped people since--well, since Steiner came across it in 1840. It appears very simple. Consider a triangle ABC with the two sides AB and AC. The angle bisector of angle B, BD is equal to the other angle bisector CE. The problem is to prove triangle ABC isosceles. Since 1840, no direct proof has been found, though almost every year a new indirect proof surfaces. In the following, I provide a direct proof of Steiner-Lehmus, using notions found only in Book 1 of _Euclid's Elements. I call it the Transamerica proof, since it looks somewhat like the Transamerica building in San Francisco. The validity of this proof has been challenged by none other than John Conway. See whether you can spot an error (I think there is none).
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