Fractals are SMART: Science, Math and Art!

Koch Curve and Coastlines

A simple geometric substitution leads to a jagged fractal much like a coastline

kochprog440

In this exercise, students learn to transform a simple shape into a complex fractal curve by repeating the same operation at smaller and smaller scales and track changes to the perimeter of the object at each step. The resulting shape is highly complex, has a large perimeter and is roughly similar to natural fractals like coastlines, snowflakes and mountain ranges.

You can use our curriculum for free or can hire us to come to your school to lead fun, hands-on activities. Check out our education and outreach page!

Ages: 3rd – 12th grades

Materials:
Pencil
Koch Curve and Coastlines worksheet
Scissors

Time:
Approx 45 minutes

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ANSWER KEY FOR TEACHERS

Teachers – if you have comments or suggestions about this or any of our other fractivities, please email us at JenFFEmailImage