Fractals: Measuring a Coastline

Andy Katz
Lawrence High School Campus

Summary

In 1967, Benoit Mandelbrot developed his concept of fractals by observing the jagged coastline of Great Britain and asking: "How do we measure such a thing?" In this lesson students will explore fractals and self-similarity, beginning with the measurement of the perimeter of a famous fractal.

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Learning Goals

Students will understand the ideas of scale and dimension with regard to fractals, and will be able to calculate the dimension of other fractals.

Context for Use

Designed for a Precalculus class, this lesson could be used - with little modification - in most levels of high school mathematics classes. This lab activity is planned for a 45 minute class or, in our case, half of a 90 minute class. Students should be familiar with measurement, tables and graphs; understanding of regression will help students generate a function. I plan to have students use Excel for tabulation and calculation.

Background

Description and Teaching Materials

In-Class Activities

At Home Assignments

Materials

1) Printed copies of Koch Snowflake
2) 4 different size "measuring sticks): 1 cm, 5 cm, 10 cm, 20 cm
3) Students will need pencils, paper and graph paper. They could also use computers and Excel.

Standards

F.BF 2: Building functions
G.GPE 3: Expressing geometric properties with equations

Teaching Notes and Tips

Assessment

References and Resources

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