For more information about this meeting, contact Augustin Banyaga, Mari Royer, Aissa Wade, Diane Henderson.
| Title: | Planimeters and isoperimetrics inequalities on constant curvature surfaces |
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| Seminar: | Symplectic Topology Seminar |
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| Speaker: | Robert Foote, Wabash College |
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| Abstract: |
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| 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 |
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| Date: | 04 / 09 / 2009 |
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| Time: | 01:25pm - 02:15pm |
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