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The Fermat-Torricelli problem once more

Published online by Cambridge University Press:  01 August 2016

Folke Eriksson
Folke Eriksson*
Affiliation:
Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden
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Extract

This extremum problem is really a classical beauty. It has had a long and interesting history since it was formulated by Fermat in the 17th century. Given three points A, B and C, the task is to find a point P such that the sum of distances PA + PB + PC is minimal; (see Figure 1). After a few years Torricelli found the solution: P should be situated so that the angles between the half-lines PA, PB and PC are all 120° (except when one angle of the triangle ABC is greater than or equal to 120°). The solution has then been rediscovered many times in new and interesting ways.

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Articles
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The Mathematical Gazette , Volume 81 , Issue 490 , March 1997, pp. 37 - 44
Copyright
Copyright © The Mathematical Association 1997

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