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  • Author or Editor: J. Januszewski x
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Parallel packing and covering of an equilateral triangle with sequences of squares

Acta Mathematica Hungarica
Volume/Issue:
Volume 125: Issue 3
DOI:
https://doi.org/10.1007/s10474-009-9015-z
Author: J. Januszewski

Abstract  

An equilateral triangle T e of sides 1 can be parallel covered with any sequence of squares whose total area is not smaller than 1:5. Moreover, any sequence of squares whose total area does not exceed

\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\frac{3} {4}(2 - \sqrt 3 )$$ \end{document}
(2 − √3) can be parallel packed into T e.

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Translative Covering by Sequences of Homothetic Copies

Acta Mathematica Hungarica
Volume/Issue:
Volume 91: Issue 4
DOI:
https://doi.org/10.1023/a:1010624119852
Author: J. Januszewski
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Translative packing of a convex body by sequences of its positive homothetic copies

Acta Mathematica Hungarica
Volume/Issue:
Volume 117: Issue 4
DOI:
https://doi.org/10.1007/s10474-007-6121-7
Author: J. Januszewski

Abstract  

Every sequence of positive homothetic copies of a planar convex body C whose total area does not exceed a quarter of the area of C can be translatively packed in C.

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