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<p>We study the geometric structure of Poncelet <i>n</i>-gons from a projective point of view. In particular we present explicit constructions of Poncelet <i>n</i>-gons for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n = 7,8\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>7</mn> <mo>,</mo> <mn>8</mn> </mrow> </math></EquationSource> </InlineEquation> and derive corresponding algebraic characterisations in terms of bracket polynomials, as well as describing a construction to produce a Poncelet 2<i>n</i>-gon from a starting Poncelet <i>n</i>-gon.</p>

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Constructing Poncelet Polygons

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月4日

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  • Leah Wrenn Berman,
  • Gábor Gévay,
  • Jürgen Richter-Gebert,
  • Serge Tabachnikov

摘要

We study the geometric structure of Poncelet n-gons from a projective point of view. In particular we present explicit constructions of Poncelet n-gons for \(n = 7,8\) n = 7 , 8 and derive corresponding algebraic characterisations in terms of bracket polynomials, as well as describing a construction to produce a Poncelet 2n-gon from a starting Poncelet n-gon.