**Measuring the Coast**

Mathematicians say that - as you look more and more closely - the California coastline becomes infinite in length. It's a type of object known as a "fractal." We'll talk with mathematician Curt McMullen about fractals - after this on Earth and Sky. **
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JB: This is Earth and Sky. A land surveyor might tell you that the California coastline has a definite length - but a mathematician would tell you otherwise. The closer you trace the coastline, the longer it gets. Mathematically speaking, the coastline is infinite - even though it doesn't go on forever. A coastline is a type of object that occurs in both nature and math known as a "fractal" or a "fractal dimension." We spoke with Harvard mathematician Dr. Curt McMullen about fractals:

(Tape 0:09:19-0:09:36) *The idea of a fractal is there are also objects which arise surprisingly often --especially when one considers natural phenomena or dynamical systems -- which are geometric in nature and they have a dimension, but the dimension is a fraction.* (Tape 0:09:51-0:10:10) *So a typical example frequently used is the idea of a coastline. So the coastline of California actually doesn't have a well-defined length because the distance from one end of the coastline to the other depends on how closely you try to navigate the coastlineā¦*(Tape 0:10:20-0:10:41) *And if you imagine not only going in and out of every inlet but going around every single pebble on the beach, you can imagine the path gets longer and longer and longer and in fact, the length of the coastline is infinite. And so we try to find a fractional number that describes the roughness or coarseness of the length of the coastline, and that's what this fractal dimension is. *

JB: Thanks to Dr. Curt McMullen for speaking with us. And with thanks to the National Science Foundation, I'm Joel Block, for Deborah Byrd, for Earth and Sky.

Author(s): Beverly Wachtel

Thanks to the following individual who aided in the preparation of this script:

Dr. Curtis McMullen

Department of Mathematics

Harvard University

Cambridge, MA

ctm@math.harvard.edu

If you enjoyed this program, you may be interested in the following:

Dr. Curtis McMullen's website:

http://www.math.harvard.edu/~ctm/

Mathematical Sciences Research Institute website:

Introduction to Fractals:

http://www.swin.edu.au/astronomy/pbourke/fractals/fracintro/

Fractals Unit for Elementary and Middle School Students:

http://math.rice.edu/~lanius/frac/