Minkowskian rhombi and squares inscribed in convex Jordan curves

Volume 120 / 2010

Horst Martini, Senlin Wu Colloquium Mathematicum 120 (2010), 249-261 MSC: Primary 52A10; Secondary 46B20, 51M04. DOI: 10.4064/cm120-2-5

Abstract

We show that any convex Jordan curve in a normed plane admits an inscribed Minkowskian square. In addition we prove that no two different Minkowskian rhombi with the same direction of one diagonal can be inscribed in the same strictly convex Jordan curve.

Authors

  • Horst MartiniFaculty of Mathematics
    TU Chemnitz
    09107 Chemnitz, Germany
    e-mail
  • Senlin WuDepartment of Applied Mathematics
    Harbin University
    of Science and Technology
    150080 Harbin, China
    e-mail

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