For more information about this meeting, contact Augustin Banyaga, Mari Royer, Aissa Wade, Diane Henderson.

Title: | Planimeters and isoperimetrics inequalities on constant curvature surfaces |

Seminar: | Symplectic Topology Seminar |

Speaker: | Robert Foote, Wabash College |

Abstract: |

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. |

### Room Reservation Information

Room Number: | MB315 |

Date: | 04 / 09 / 2009 |

Time: | 01:25pm - 02:15pm |