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<p>Richelot, F., in the Journal für die reine und angewandte Mathematik, 250–267 (1830) developed the Fuss formulae for bicentric polygons of high order, circuminscribed between two circles. In particular, he demonstrated a doubling technique for deriving the formulae for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( 2n \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation>-sided polygons, from the formulae for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( n \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>n</mi> </math></EquationSource> </InlineEquation>-sided polygons.</p><p>While reviewing and implementing these results from 1830, we noticed that the formulae were not producing closed polygons. Upon further inspection, we uncovered the errant typos and fixed them.</p>

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The Fuss About Fuss

  • 期刊论文

  • 发表日期：

    2026年3月4日

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  • Aharon Naiman,
  • Waldemar Cieślak,
  • Witold Mozgawa

摘要

Richelot, F., in the Journal für die reine und angewandte Mathematik, 250–267 (1830) developed the Fuss formulae for bicentric polygons of high order, circuminscribed between two circles. In particular, he demonstrated a doubling technique for deriving the formulae for \( 2n \) 2 n -sided polygons, from the formulae for \( n \) n -sided polygons.

While reviewing and implementing these results from 1830, we noticed that the formulae were not producing closed polygons. Upon further inspection, we uncovered the errant typos and fixed them.