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<p>Denote by <i>H</i> a regular hexagon with sides of length 1. Let <i>S</i> be a square with a side parallel to a side of <i>H</i> and let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\{S_{n}\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <msub> <mi>S</mi> <mi>n</mi> </msub> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation> be a collection of the homothetic copies of <i>S</i>. In this note a tight lower bound of the sum of the areas of squares from <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\{S_{n}\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <msub> <mi>S</mi> <mi>n</mi> </msub> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation> that can parallel cover <i>H</i> is determined.</p>

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Parallel covering a regular hexagon with squares

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • Ziyi Guo,
  • Zhanjun Su

摘要

Denote by H a regular hexagon with sides of length 1. Let S be a square with a side parallel to a side of H and let \(\{S_{n}\}\) { S n } be a collection of the homothetic copies of S. In this note a tight lower bound of the sum of the areas of squares from \(\{S_{n}\}\) { S n } that can parallel cover H is determined.