Affinely Regular Polygons as Extremals of Area Functionals

Twentieth Anniversary Volume: ◽

10.1007/978-0-387-87363-3_15 ◽

2008 ◽

pp. 1-25

Author(s):

Paolo Gronchi ◽

Marco Longinetti

Keyword(s):

Regular Polygons ◽

Affinely Regular Polygons

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Affinely Regular Polygons as Extremals of Area Functionals

Discrete & Computational Geometry ◽

10.1007/s00454-007-9010-5 ◽

2007 ◽

Vol 39 (1-3) ◽

pp. 273-297 ◽

Cited By ~ 6

Author(s):

Paolo Gronchi ◽

Marco Longinetti

Keyword(s):

Regular Polygons ◽

Affinely Regular Polygons

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Affinely regular polygons

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg ◽

10.1007/bf02992886 ◽

1969 ◽

Vol 34 (1-2) ◽

pp. 38-58 ◽

Cited By ~ 15

Author(s):

H. S. M. Coxeter

Keyword(s):

Regular Polygons ◽

Affinely Regular Polygons

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A characterization of affinely regular polygons

Aequationes Mathematicae ◽

10.1007/s00010-018-0541-z ◽

2018 ◽

Vol 92 (6) ◽

pp. 1037-1049

Author(s):

Zsolt Lángi

Keyword(s):

Regular Polygons ◽

Affinely Regular Polygons

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A note on affinely regular polygons

European Journal of Combinatorics ◽

10.1016/j.ejc.2008.05.001 ◽

2009 ◽

Vol 30 (2) ◽

pp. 387-395 ◽

Cited By ~ 3

Author(s):

Christian Huck

Keyword(s):

Regular Polygons ◽

Affinely Regular Polygons

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A characterization of affinely regular polygons

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry ◽

10.1007/s13366-015-0271-5 ◽

2015 ◽

Vol 57 (2) ◽

pp. 453-458 ◽

Cited By ~ 2

Author(s):

Grégoire Nicollier

Keyword(s):

Regular Polygons ◽

Affinely Regular Polygons

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Dense Periodic Packings of Regular Polygons

Journal de Physique I ◽

10.1051/jp1:1995112 ◽

1995 ◽

Vol 5 (12) ◽

pp. 1539-1550 ◽

Cited By ~ 4

Author(s):

Y. Limon Duparcmeur ◽

A. Gervois ◽

J. P. Troadec

Keyword(s):

Regular Polygons

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Random Close Packings of Regular Polygons

Journal de Physique I ◽

10.1051/jp1:1997115 ◽

1997 ◽

Vol 7 (10) ◽

pp. 1181-1189 ◽

Cited By ~ 6

Author(s):

Y. Limon Duparcmeur ◽

J. P. Troadec ◽

A. Gervois

Keyword(s):

Regular Polygons

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New Theorems for Moments of Inertia

International Journal of Mechanical Engineering Education ◽

10.1177/030641909302100406 ◽

1993 ◽

Vol 21 (4) ◽

pp. 355-366 ◽

Cited By ~ 1

Author(s):

David L. Wallach

Keyword(s):

Regular Polygon ◽

Moment Of Inertia ◽

Regular Polygons ◽

Centre Of Mass ◽

Moments Of Inertia ◽

The Moment

The moment of inertia of a plane lamina about any axis not in this plane can be easily calculated if the moments of inertia about two mutually perpendicular axes in the plane are known. Then one can conclude that the moments of inertia of regular polygons and polyhedra have symmetry about a line or point, respectively, about their centres of mass. Furthermore, the moment of inertia about the apex of a right pyramid with a regular polygon base is dependent only on the angle the axis makes with the altitude. From this last statement, the calculation of the centre of mass moments of inertia of polyhedra becomes very easy.

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