AN EXTREMAL VALUE PROBLEM CONCERNING THE INSCRIBED SPHERE OF PYRAMIDS

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Abstract

Consider the following question: In a circular cone, with the sum of the radius of the base circle and the length of the bus line being 1, the inscribed sphere is to be maximal. How much is the radius of the base circle? It is easy to see that the answer is 1/3, which is geometrically interpreted as follows: Consider the section of a cone by a plane which contains the apex and is perpendicular to the base circle. Then the answer corresponds to the case that the section is an equilateral triangle. In this paper, we generalize the question to the case that the base circle is generalized to regular polygons.

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Journal

  • Ryukyu mathematical journal

    Ryukyu mathematical journal 27 9-17, 2014-12-26

    Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus

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