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The Fermat-Torricelli Problem of Triangles on the Sphere with Euclidean Metric: A Symbolic Solution with Maple

  • Xiaofeng Guo
  • Tuo Leng
  • Zhenbing ZengEmail author
Conference paper
  • 43 Downloads
Part of the Communications in Computer and Information Science book series (CCIS, volume 1125)

Abstract

The Fermat-Torricelli problem of triangles on the sphere under Euclidean metric asks to find the optimal point P on the sphere \(S^2\) for three given points ABC on \(S^2\), so that the sum of the Euclidean distances \(L=PA+PB+PC\) from that point P to the three vertices is minimal (or maximal). In this paper we introduce a solution to this problem done with help of the symbolic computation software Maple and interpolation of implicit function, where the minimal and the maximal sum of the distances are expressed by same polynomial f(Labc) of degree 12 with \(a=BC, b=CA, c=AB\).

Keywords

Fermat-Torricelli problem Elimination Sylvester resultant Dixon resultant Implicit function interpolation Symbolic-Numeric hybrid computation 

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiChina
  2. 2.School of Computer Engineering and ScienceShanghai UniversityShanghaiChina
  3. 3.School of Mathematical SciencesEast China Normal UniversityShanghaiChina

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