Title

Brunn-Minkowski Theory and Cauchy's Surface Area Formula

SMC Author

Ellen Veomett

SMC Affiliated Work

1

Status

Faculty

School

School of Science

Department

Math/Computer Science

Document Type

Article

Publication Date

12-2017

Publication Title

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.

Share

COinS