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.
Original language | American English |
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Journal | The American Mathematical Monthly |
Volume | 124 |
DOIs | |
State | Published - Dec 1 2017 |
Keywords
- Surface areas
- Mathematical theorems
- Mathematical vectors
- Mathematical inequalities
- Mathematical notation
- Hausdorff measures
- College mathematics
Disciplines
- Computer Sciences
- Mathematics