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  • 1 Universidad de Guanajuato Facultad de Matemáticas Guanajuato México
  • 2 Instituto de Matemáticas Universidad Nacional Autónoma de México Acapulco México
  • 3 Universidad Autónoma de Guerrero Facultad de Matemáticas Acapulco México
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Abstract  

In this paper the following is proved: let

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}$$ \end{document}
be a centrally symmetric set of points, such that the distance between any pair of points is at least 1 and every three of them can be covered by a strip of width 1. Then there is a strip of width √2 covering
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{P}$$ \end{document}
.

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