Geometric characterizations of centroids of simplices

Steven G. Krantz; John E. McCarthy; Harold R. Parks

doi:10.1016/j.jmaa.2005.04.046

Geometric characterizations of centroids of simplices

Steven G. Krantz, John E. McCarthy, Harold R. Parks

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16 Scopus citations

Abstract

We study the centroid of a simplex in space. Primary attention is paid to the relationships among the centroids of the different k-skeletons of a simplex in n-dimensional space. We prove that the 0-dimensional skeleton and the n-dimensional skeleton always have the same centroid. The centroids of the other skeleta are generically different (as we prove), but there are remarkable instances where they coincide in pairs. They never coincide in triples for regular pyramids.

Original language	English
Pages (from-to)	87-109
Number of pages	23
Journal	Journal of Mathematical Analysis and Applications
Volume	316
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2005.04.046
State	Published - Apr 1 2006

Keywords

Centroid
Dynamics
Polytope
Pyramid
Rigid body
Simplex

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10.1016/j.jmaa.2005.04.046

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title = "Geometric characterizations of centroids of simplices",

abstract = "We study the centroid of a simplex in space. Primary attention is paid to the relationships among the centroids of the different k-skeletons of a simplex in n-dimensional space. We prove that the 0-dimensional skeleton and the n-dimensional skeleton always have the same centroid. The centroids of the other skeleta are generically different (as we prove), but there are remarkable instances where they coincide in pairs. They never coincide in triples for regular pyramids.",

keywords = "Centroid, Dynamics, Polytope, Pyramid, Rigid body, Simplex",

author = "Krantz, {Steven G.} and McCarthy, {John E.} and Parks, {Harold R.}",

note = "Funding Information: * Corresponding author. E-mail address: sk@math.wustl.edu (S.G. Krantz). 1 Partially supported by National Science Foundation Grant DMS 03222551.",

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AU - Krantz, Steven G.

AU - McCarthy, John E.

AU - Parks, Harold R.

N1 - Funding Information: * Corresponding author. E-mail address: sk@math.wustl.edu (S.G. Krantz). 1 Partially supported by National Science Foundation Grant DMS 03222551.

PY - 2006/4/1

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N2 - We study the centroid of a simplex in space. Primary attention is paid to the relationships among the centroids of the different k-skeletons of a simplex in n-dimensional space. We prove that the 0-dimensional skeleton and the n-dimensional skeleton always have the same centroid. The centroids of the other skeleta are generically different (as we prove), but there are remarkable instances where they coincide in pairs. They never coincide in triples for regular pyramids.

AB - We study the centroid of a simplex in space. Primary attention is paid to the relationships among the centroids of the different k-skeletons of a simplex in n-dimensional space. We prove that the 0-dimensional skeleton and the n-dimensional skeleton always have the same centroid. The centroids of the other skeleta are generically different (as we prove), but there are remarkable instances where they coincide in pairs. They never coincide in triples for regular pyramids.

KW - Centroid

KW - Dynamics

KW - Polytope

KW - Pyramid

KW - Rigid body

KW - Simplex

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DO - 10.1016/j.jmaa.2005.04.046

M3 - Article

AN - SCOPUS:29944432473

SN - 0022-247X

VL - 316

SP - 87

EP - 109

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Geometric characterizations of centroids of simplices

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Keywords

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