Critical Chords of Convex Bodies of Constant Width

In this paper, we show that when Minkowski measure of asymmetry of convex body K of constant width is bigger than α ( n -1), K has at least n +1 critical chords, where α ( n ) = n + 2 n ( n + 1 ) n + 2 .

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Bibliographic Details
Published inWuhan University journal of natural sciences Vol. 23; no. 6; pp. 461 - 464
Main Authors Zhou, Xinyue, Jin, Hailin
Format Journal Article
LanguageEnglish
Published Wuhan Wuhan University 01.12.2018
Springer Nature B.V
Subjects
Biomedical and Life Sciences
Chords (geometry)
Computer Science
Life Sciences
Materials Science
constant width
measure of asymmetry
Grünbaum conjecture
affine diameter
O 186
critical chord
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Summary:In this paper, we show that when Minkowski measure of asymmetry of convex body K of constant width is bigger than α ( n -1), K has at least n +1 critical chords, where α ( n ) = n + 2 n ( n + 1 ) n + 2 .
ISSN:1007-1202
1993-4998
DOI:10.1007/s11859-018-1348-4