Brunn-Minkowski Theory and Cauchy's Surface Area Formula
SMC Affiliated Work
1
Status
Faculty
School
School of Science
Department
Math/Computer Science
Document Type
Article
Publication Date
12-2017
Publication / Conference / Sponsorship
The American Mathematical Monthly
Description/Abstract
We use Brunn-Minkowski theory and well-known integration tools to prove Cauchy’s surface area formula, which states that the average area of a projection of a convex body is equal to its surface area up to a multiplicative constant in the dimension. Using the same technique, we give a straightforward extension to intrinsic moment vectors of a convex body.
Keywords
Surface areas, Mathematical theorems, Mathematical vectors, Mathematical inequalities, Mathematical notation, Hausdorff measures, College mathematics
Scholarly
yes
DOI
10.4169/amer.math.monthly.124.10.922
Volume
124
Issue
10
First Page
922
Last Page
929
Disciplines
Computer Sciences | Mathematics
Original Citation
Tsukerman, E. Veomett, E. “Brunn-Minkowski Theory and Cauchy's Surface Area Formula.” American Mathematical Monthly, 124(10),922-929. December 2017. DOI: 10.4169/amer.math.monthly.124.10.922.
Repository Citation
Tsukerman, Emmanuel and Veomett, Ellen. Brunn-Minkowski Theory and Cauchy's Surface Area Formula (2017). The American Mathematical Monthly. 124 (10), 922-929. 10.4169/amer.math.monthly.124.10.922 [article]. https://digitalcommons.stmarys-ca.edu/school-science-faculty-works/170
