Vectorial analogues of Cauchy’s surface area formula
Vectorial analogues of Cauchy’s surface area formula
Abstract Cauchy’s surface area formula says that for a convex body K in n -dimensional Euclidean space, the mean value of the $$(n-1)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -dimensional volumes of the orthogonal projections of K to hyperplanes is a constant multiple of the surface …