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On the Circumradius of a Special Class of n-Simplices

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Abstract

An n-simplex is called circumscriptible (or edge-incentric) if there is a sphere which is tangent to all its n(n + 1)/2 edges. We obtain a closed formula for the radius of the circumscribed sphere of a circumscriptible n-simplex, and we prove a double inequality involving the circumradius and the edge-inradius of such simplices. With these results a part of a problem posed by the authors is solved.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Xinchang High School, Shaoxing, 312500, Zhejiang, People’s Republic of China

    Yu-Dong Wu

  2. Department of Mathematics, Shili Senior High School in Zixing, Chenzhou, 423400, Hunan, People’s Republic of China

    Zhi-Hua Zhang

Authors
  1. Yu-Dong Wu
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  2. Zhi-Hua Zhang
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Correspondence to Yu-Dong Wu.

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Dedicated to Professor Lu Yang

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Wu, YD., Zhang, ZH. On the Circumradius of a Special Class of n-Simplices. Results. Math. 61, 29–42 (2012). https://doi.org/10.1007/s00025-010-0073-x

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  • DOI: https://doi.org/10.1007/s00025-010-0073-x

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