Brunn-Minkowski Theory and Cauchy's Surface Area Formula

Emmanuel Tsukerman, Ellen Veomett

Research output: Contribution to journalArticlepeer-review


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 languageAmerican English
JournalThe American Mathematical Monthly
StatePublished - Dec 1 2017


  • Surface areas
  • Mathematical theorems
  • Mathematical vectors
  • Mathematical inequalities
  • Mathematical notation
  • Hausdorff measures
  • College mathematics


  • Computer Sciences
  • Mathematics

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