Involve: A Journal of Mathematics

  • Involve
  • Volume 8, Number 5 (2015), 771-785.

Generalizations of Pappus' centroid theorem via Stokes' theorem

Cole Adams, Stephen Lovett, and Matthew McMillan

Full-text: Open access

Abstract

This paper provides a novel proof of a generalization of Pappus’ centroid theorem on n-dimensional tubes using Stokes’ theorem on manifolds.

Article information

Source
Involve, Volume 8, Number 5 (2015), 771-785.

Dates
Received: 18 March 2014
Accepted: 22 November 2014
First available in Project Euclid: 22 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.involve/1511370948

Digital Object Identifier
doi:10.2140/involve.2015.8.771

Mathematical Reviews number (MathSciNet)
MR3404657

Zentralblatt MATH identifier
1325.53013

Subjects
Primary: 53A07: Higher-dimensional and -codimensional surfaces in Euclidean n-space 58C35: Integration on manifolds; measures on manifolds [See also 28Cxx]

Keywords
Stokes' theorem on manifolds volume manifolds tubes

Citation

Adams, Cole; Lovett, Stephen; McMillan, Matthew. Generalizations of Pappus' centroid theorem via Stokes' theorem. Involve 8 (2015), no. 5, 771--785. doi:10.2140/involve.2015.8.771. https://projecteuclid.org/euclid.involve/1511370948


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References

  • M. C. Domingo-Juan and V. Miquel, “Pappus type theorems for motions along a submanifold”, Differential Geom. Appl. 21:2 (2004), 229–251.
  • A. W. Goodman and G. Goodman, “Generalizations of the theorems of Pappus”, Amer. Math. Monthly 76 (1969), 355–366.
  • A. Gray and V. Miquel, “On Pappus-type theorems on the volume in space forms”, Ann. Global Anal. Geom. 18:3-4 (2000), 241–254.
  • S. Lovett, Differential geometry of manifolds, A K Peters, Natick, MA, 20\hskip -0.1mm10. http://msp.org/idx/mr/2011k:53001MR 2011k:53001