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<p>The celebrated Poncelet porism is usually studied for a pair of smooth conics that are in a general position. Here we discuss Poncelet porism in the real plane — affine or projective, when that is not the case, i. e., the conics have at least one point of tangency or at least one of the conics is not smooth.In all such cases, we find necessary and sufficient conditions for the existence of an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\)</EquationSource> </InlineEquation>-gon inscribed in one of the conics and circumscribed about the other.</p>

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Poncelet Porism in Singular Cases

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Vladimir Dragović,
  • Milena Radnović

摘要

The celebrated Poncelet porism is usually studied for a pair of smooth conics that are in a general position. Here we discuss Poncelet porism in the real plane — affine or projective, when that is not the case, i. e., the conics have at least one point of tangency or at least one of the conics is not smooth.In all such cases, we find necessary and sufficient conditions for the existence of an \(n\) -gon inscribed in one of the conics and circumscribed about the other.