#### Title

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