# Meeting Details

Title: Planimeters and isoperimetrics inequalities on constant curvature surfaces Topology/Geometry Seminar Robert Foote, Wabash College The well-known isoperimetric inequality states that $4\pi A \le L^2$, where $A$ is the area of a region in the Euclidean plane and $L$ is the length of its boundary. The corresponding inequality for regions on the sphere or in the hyperbolic plane is $4\pi A - kA^2 \le L^2$, where $k$ is the curvature of the surface. A planimeter is a simple mechanical instrument used to determine the area of a planar region by tracing around its boundary. I will show how one works, including on the sphere and hyperbolic plane, and use the ideas involved to give a novel proof of some stronger Bonnesen isoperimetric inequalities on these surfaces. Some planimeters will be available for those who want to try one.