the negative Fermat point. However these different names can be confusing and are perhaps best avoided. The problem is that much of the literature blurs the distinction between the Fermat point and the first Fermat point whereas it is only in Case 2 above that they are actually the same. History This question was proposed by Fermat, as a challenge to Evangelista Torricelli. He solved the problem in a similar way to Fermat's, albeit using the intersection of the circumcircles of the three regular triangles instead. His pupil, Viviani, published the solution in 1659. See also Geometric median or Fermat–Weber point, the point minimizing the sum of distances to more than three given points. Lester's theorem Triangle center Napoleon points Weber problem References External links Fermat Point by Chris Boucher, The Wolfram Demonstrations Project. Fermat-Torricelli generalization at Dynamic Geometry Sketches Interactive sketch generalizes the Fermat-Torricelli point. A practical example of the Fermat point iOS Interactive sketch Triangle centers Articles containing proofs