Advertisement

Applied Mathematics and Mechanics

, Volume 8, Issue 10, pp 969–974 | Cite as

The Steiner problem on a surface

  • Jiang Xin-yao
Article

Abstract

In this paper we generalize the Steiner problem on planes to general regular surfaces. The main result is

Theorem 1 If A,B,C are three points on a regular surface Σ and if another point P on Σ such that the sum of the lengths of the smooth arcs Open image in new window reaches the minimum, then the angles formed by every two arcs at P are all 120°.

Keywords

Connected Graph Minimal Tree Steiner Point Unit Tangent Vector Regular Surface 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Courant, R. and H. Robbins,What Is Mathematics? Chapter 7, § 5, Oxford University Press, New York (1964).Google Scholar
  2. [2]
    Kline, Morris,Mathematical Thought form Ancient to Times, Oxford Univ. Press, New York (1972).Google Scholar
  3. [3]
    Melzak, Z.A., On the problem of Steiner,Ganad. Math. Bull.,4 (1961), 143–148.zbMATHMathSciNetGoogle Scholar
  4. [4]
    Pollak, H.O., Some remarks on the Steiner problem,J. Combinational Thy.,A,24 (1978), 278–295.zbMATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Wang Kai-ning, The elementary proof of Fermat point problem in convexn sides polygon,The Journal of University of Science and Technology of China,11, 4 (1981), 139–141. (in Chinese)Google Scholar
  6. [6]
    Huang Guang-ming, Shortest network,Journal of Operational Research,2, 2 (1983), 18–25. (in Chinese)Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1987

Authors and Affiliations

  • Jiang Xin-yao
    • 1
  1. 1.Shanghai University of TechnologyShanghai

Personalised recommendations