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<p>In this paper, we study a Poncelet-type problem concerning the number of convex <i>n</i>-gons that can be inscribed in one convex <i>n</i>-gon and circumscribed about another. We prove that this number is at most four, and that the bound is sharp. This contrasts with Poncelet-type porisms, where the existence of a single such polygon usually implies the existence of infinitely many.</p>

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The Number of Inscribed and Circumscribed Polygons of a Convex Polygon

  • 期刊论文

  • 发表日期：

    2025年9月16日

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  • Yagub N. Aliyev

摘要

In this paper, we study a Poncelet-type problem concerning the number of convex n-gons that can be inscribed in one convex n-gon and circumscribed about another. We prove that this number is at most four, and that the bound is sharp. This contrasts with Poncelet-type porisms, where the existence of a single such polygon usually implies the existence of infinitely many.