Tearing Plastic

 

A Laboratory Exercise on Fractals and Hyperbolic Geometry

A website to accompany an article for PRIMUS

by Ron Taylor and Todd Timberlake
[Overview] [Activity Handout] [Pictures]


Overview

This website is intended to supplement an article that was published in PRIMUS. In the article we describe a hands-on activity for a liberal arts mathematics course that focuses on the beauty and unity of mathematics rather than its utility. The purpose of the activity is to tie together several topics in the context of a “real-world” situation. These topics include: fractals, non-Euclidean geometry, symmetry and Platonic solids. This activity would also be appropriate for a geometry course.

This activity was derived from an article from American Scientist magazine, entitled “Leaves, Flowers, and Garbage Bags: Making Waves” by Sharon, Marder, and Swinney. That article is available online through this link on the American Scientist website.


Activity Handout

Use the links below to download the handout we developed for this activity. The handout is available in PDF format, and also as LaTeX source. Feel free to edit the LaTeX source to better fit the particulars of your class.


Pictures

The images below show completed portions of the activity.
Here are three pictures of the edges of the torn plastic sheets (using three different types of plastic):

torn_edge3

torn_edge2

torn_edge1

 

Here’s an image showing the grid with lines on the torn plastic sheet, before and after the sheet is torn:

grid_w_lines stretched_w_lines1

Finally, here’s a portion of a hyperbolic surface constructed from equilateral triangles:

hyperbolic_surface

If you have any questions about these materials, please email Todd Timberlake at ttimberlake@berry.edu or Ron Taylor at rtaylor@berry.edu.