Fractals: Measuring a Coastline
Andy Katz
Lawrence High School Campus
Initial Publication Date: June 6, 2018
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
Fractals: Measuring a Coastline --Discussion
Hello Andy -
I thought this sounded like promising terrain to explore when you talked about it in class. I look forward to reading more about how you plan to structure an investigation for students, and what they figure out!
Ellen
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edittextuser=3872 post_id=18318 initial_post_id=0 thread_id=5424
Andy, I really like this - I think it will help your students understand fractals (the word is so common these days). I wish my teachers had done it with me.
Lindy
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edittextuser=3776 post_id=18337 initial_post_id=0 thread_id=5424
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