Real World Math: Measurement - Fractal Coastline

This lesson follows the idea put forth by Benoit Mandelbrot in his 1967 paper “How Long is the Coast of Britain?”  Mandelbrot pioneered the study of fractals, and in this paper he proposed that the length of any measure is related to the scale of measurement used. 

In theory, the coastline of Britain is infinite.

To test this theory, students will measure the distance between two marked points on the southern coast of Britain from different elevations in Google Earth.  Using the ruler tool set on “path” mode, the students should try to measure the coastline including all the bays and points.  The exercise is repeated at different elevations by selecting the numbered placemarks in succession.  At the lowest elevation, the students will have to move the Google Earth map as they use the ruler tool.  They should find that as they become more exact in their measures, the distance between the marked points gets larger.  What would it take to get a definitive measure?

One possible discussion that could follow this exercise would be that on degree of accuracy when measuring.  Another, would be on the fractal appearance of the selected view at different elevations.  Fractals show self-similarity at any scale.  Did this hold true with the coastline?

Objectives

  • Explore accuracy of measurement
  • Measure nonlinear distance
  • Explore the concept of fractals

Measurement & Time
Middle School, Educator

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