TY - JOUR
T1 - Brunn-Minkowski Theory and Cauchy's Surface Area Formula
AU - Tsukerman, Emmanuel
AU - Veomett, Ellen
PY - 2017/12/1
Y1 - 2017/12/1
N2 - 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.
AB - 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.
KW - Surface areas
KW - Mathematical theorems
KW - Mathematical vectors
KW - Mathematical inequalities
KW - Mathematical notation
KW - Hausdorff measures
KW - College mathematics
UR - https://digitalcommons.stmarys-ca.edu/school-science-faculty-works/170
UR - https://doi.org/10.4169/amer.math.monthly.124.10.922
U2 - 10.4169/amer.math.monthly.124.10.922
DO - 10.4169/amer.math.monthly.124.10.922
M3 - Article
VL - 124
JO - The American Mathematical Monthly
JF - The American Mathematical Monthly
ER -