Fermat’s Problem in Banach-Minkowski Spaces

  • Dietmar Cieslik
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 23)


The following problem was posed by Fermat early in the 17th century: Given three points in the plane, find a fourth point such that the sum of its distances to the three given points is a minimum. Torricelli solved this problem in 1646. He asserted that the circles that circumscribe the equilateral triangles constructed on the side of and outside of the given triangle intersect in the desired point, called the Torricelli point.


Convex Hull Unit Ball Convex Body Euclidean Plane Steiner Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Dietmar Cieslik
    • 1
  1. 1.Ernst-Moritz-Arndt UniversityGreifswaldGermany

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