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Zbl 0901.51010
Krarup, Jakob; Vajda, Steven
On Torricelli's geometrical solution to a problem of Fermat. (English)
[J] IMA J. Math. Appl. Bus. Ind. 8, No.3, 215-224 (1997). ISSN 0953-0061

Summary: Around 1640, Torricelli devised a geometrical solution to a problem, allegedly first formulated in the early 1600s by Fermat: `given three points in a plane, find a fourth point such that the sum of its distances to the three given points is as small as possible'. We account for Torricelli's construction together with a correctness proof which also establishes the validity of results obtained much later. We introduce furthermore a so-called complementary problem, arising when the given triangle has one angle exceeding $120^\circ$, and for which an incorrect solution was given in 1941 by Courant \& Robbins. Some historical notes conclude the paper.

MSC 2000:: *51M04 Elementary problems in Euclidean geometries
90B85 Continuous location
90C33 Complementarity problems

Keywords: triangle; minimal distance

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