Article
Brunn-Minkowski Theory and Cauchy's Surface Area Formula
The American Mathematical Monthly
Status
Faculty
School
School of Science
Department
Math/Computer Science
Document Type
Article
Publication Date
12-1-2017
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
Disciplines
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.
Citation Information
Emmanuel Tsukerman and Ellen Veomett. "Brunn-Minkowski Theory and Cauchy's Surface Area Formula" The American Mathematical Monthly Vol. 124 Iss. 10 (2017) p. 922 - 929 Available at: http://works.bepress.com/ellen-veomett/7/