960 On a proof I learned from prof. dr. J. Haantjes

Amarillo, 22 May 1986. 3 pages. transcription.

Description of a proof from prof. dr. J. Haantjes that the altitudes in a triangle are concurrent.

Contrasted with the clumsy Euclidean proof on which the author had been educated, which uses the concurrency of the angle bisectors of a triangle, instead of depending on the symmetry and associativity of addition and multiplication.

Proof is simplified at the end. The author expresses amazement that even though he often used this proof as example of an “ingeniously simple and effective” argument, it took him more than 37 years to discover this simplification.