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

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Maple in Mathematics Education and Research (MC 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1125))

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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 A, B, C 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(L, a, b, c) of degree 12 with \(a=BC, b=CA, c=AB\).

Support by the Chinese National Natural Science Foundation (11471209 and 11501352).

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Author information

Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Xiaofeng Guo & Zhenbing Zeng

  2. School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China

    Tuo Leng

  3. School of Mathematical Sciences, East China Normal University, Shanghai, 200062, China

    Xiaofeng Guo

Authors
  1. Xiaofeng Guo
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  2. Tuo Leng
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  3. Zhenbing Zeng
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Corresponding author

Correspondence to Zhenbing Zeng .

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Editors and Affiliations

  1. Maplesoft, Waterloo, ON, Canada

    Jürgen Gerhard

  2. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias Kotsireas

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Guo, X., Leng, T., Zeng, Z. (2020). The Fermat-Torricelli Problem of Triangles on the Sphere with Euclidean Metric: A Symbolic Solution with Maple. In: Gerhard, J., Kotsireas, I. (eds) Maple in Mathematics Education and Research. MC 2019. Communications in Computer and Information Science, vol 1125. Springer, Cham. https://doi.org/10.1007/978-3-030-41258-6_20

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  • DOI: https://doi.org/10.1007/978-3-030-41258-6_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-41257-9

  • Online ISBN: 978-3-030-41258-6

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