Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (2): 491-501.doi: 10.1007/s10473-022-0204-y

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ON THE BOUNDS OF THE PERIMETER OF AN ELLIPSE

Tiehong ZHAO1, Miaokun WANG2, Yuming CHU2   

  1. 1. Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China;
    2. Department of Mathematics, Huzhou University, Huzhou 313000, China
  • Received:2020-05-24 Revised:2021-06-05 Online:2022-04-25 Published:2022-04-22
  • Supported by:
    This research was supported by the Natural Science Foundation of China (11971142) and the Natural Science Foundation of Zhejiang Province (LY19A010012).

Abstract: In this paper, we present new bounds for the perimeter of an ellipse in terms of harmonic, geometric, arithmetic and quadratic means; these new bounds represent improvements upon some previously known results.

Key words: Gaussian hypergeometric function, complete elliptic integral, ellipse, perimeter

CLC Number: 

  • 26E60
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