## The Isoperimetric Inequality |

**Christina Tonnesen-Friedman**

Union College

November 1, 2011

4:45 pm

Bailey Hall 207

Refreshments will be served in Bailey Hall 204 at 4:30

Among all closed non-self-intersecting planar curves of a fixed length, the circle encloses the maximum area. When you think about this for a bit, it probably seems intuitively clear. However, the proof is not a simple as one might guess.I will describe two classical proofs; a very geometric one (with one fatal flaw) and then a complete calculus proof using Green’s Theorem. The former doesn’t really require any background knowledge other than basic geometry, while the latter uses double integrals (and area), line integrals, and Green’s Theorem.

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Union College Math Department Home PageComments to: math@union.edu Created automatically on: Fri Jul 20 16:30:05 EDT 2018 |