##### Department of Mathematics,

University of California San Diego

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### Math 196/296 - Student Colloquium

## Carl FitzGerald

#### UCSD

## The isoperimetric problem solved one dimension at a time

##### Abstract:

Among quadrilaterals with sides of specified lengths, there is a unique quadrilateral that encloses the maximum possible area. This extremal quadrilateral is cyclic, that is, its vertices lie on a circle. The extremal pentagons are also cyclic. In general, n-sided polygons with sides of specified lengths that enclose the maximum area are cyclic. These facts are used to solve the isoperimetric problem: Among closed plane curves of length $L$, find the curves that enclose the maximum area. Solution: the circles of length $L$. \vskip 3in

Host:

### November 3, 2005

### 11:00 AM

### AP&M 2402

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