On the Diameter of a Circle to Hold a Cube

It is proved that a circle of diameter d can hold a cube of unit edge if and only if $\sqrt2\le d< 1.53477...$ . Similarly, it can be proved that a circle of diameter d can hold a regular octahedron of unit edge if and only if 1 ≤ d < 1.1066...

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Bibliographic Details
Published inComputational Geometry, Graphs and Applications Vol. 7033; pp. 147 - 153
Main Author Maehara, Hiroshi
Format Book Chapter
LanguageEnglish
Published Germany Springer Berlin / Heidelberg 2011
Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
52A15
52B10
52C99
Algorithms & data structures
cube
Discrete mathematics
Graphics programming
holding circle
octahedron
Online AccessGet full text
ISBN9783642249822
3642249825
ISSN0302-9743
1611-3349
DOI10.1007/978-3-642-24983-9_15

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Summary:It is proved that a circle of diameter d can hold a cube of unit edge if and only if $\sqrt2\le d< 1.53477...$ . Similarly, it can be proved that a circle of diameter d can hold a regular octahedron of unit edge if and only if 1 ≤ d < 1.1066...
Bibliography:Original Abstract: It is proved that a circle of diameter d can hold a cube of unit edge if and only if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt2\le d< 1.53477...$\end{document}. Similarly, it can be proved that a circle of diameter d can hold a regular octahedron of unit edge if and only if 1 ≤ d < 1.1066....
ISBN:9783642249822
3642249825
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-642-24983-9_15