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Parallel covering a regular hexagon with squares
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DOI：10.1007/s10474-026-01591-1.png)
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Abstract
En 中文
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 {Sn}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{S_{n}\}$$\end{document} 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 {Sn}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{S_{n}\}$$\end{document} that can parallel cover H is determined.
Keywords:
Parallel covering
Regular hexagon
Square