Cynthia Lanius

    Why Study Fractals?

What's so hot about fractals, anyway?

They're New!

Most math you study in school is old knowledge. For example, the geometry you study about circles, squares, and triangles was organized around 300 B.C. by a man named Euclid.Fractal geometry, however, is much newer. Research on fractals is being carried out right now by mathematicians. Have you ever thought about a career as a mathematician?

You can understand them.

Much research in mathematics is currently being done all over the world. Although we need to study and learn more before we can understand most modern mathematics, there's a lot about fractals that we can understand.

Fractals often look like objects in nature.

Many objects in nature aren't formed of squares or triangles, but of more complicated geometric figures. Many natural objects - ferns, coastlines, etc. - are shaped like fractals. This picture is actually an example of a fractal.

Look at another example below.

Imagine the picture to the right is a picture of the coastline of Africa.You measure it with mile-long rulers and get a certain measurement. What if on the next day you measure it with foot-long rulers? Which measurement would give you a larger measurement. Since the coastline is jagged, you could get into the nooks and crannies better with the foot-long ruler, so it would yield a greater measurement. Now what if you measured it with an inch-long ruler? You could really get into the teeniest and tiniest of crannies there. So the measurement would be even bigger, that is if the coastline is jagged smaller than an inch. What if it were jagged at every point on the coastline? You could measure it with shorter and shorter rulers, and the measurement would get longer and longer. You could even measure it with infinitesimally short rulers, and the coastline would be infinitely long. That's fractal.

Internet Research Questions:

  1. Who organized geometry into a series of books? What are those books called?

  2. What is the name of a mathematician who does research today? Where does he/she work? What is the area of mathematics in which he/she works?

  3. Find another picture of a fractal that looks like an object in nature.
If possible, email me your answers.

lanius@math.rice.edu

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Copyright 1996-2007 Cynthia Lanius
URL http://math.rice.edu/~lanius/fractals/WHY/inpr.html