Steiner's formula and a variational proof of the isoperimetric inequality
Steiner's formula and a variational proof of the isoperimetric inequality
We give a new proof of the isoperimetric inequality in the plane, based on Steiner's formula for the area of a convex neighborhood. This proof establishes the isoperimetric inequality directly, without requiring that we separately establish the existence of an optimal domain. In doing so, this proof bypasses the main …