Geometry in Nature

By Anne Marie Burdick

Walking around the Rory Meyers Children’s Adventure Garden at the Dallas Arboretum, I could not help but to turn into a child again. As I navigated through the different exhibits on nature I soon found myself in the Kaleidoscope gallery. Here I had the opportunity to discover how geometry can be found in nature. This particular display demonstrated how there are patterns, tessellations, and fractals throughout nature. During my visit to the arboretum, I decided to focus my attention on fractals in nature. A fractal is a pattern that constantly repeats itself. Fractals can be found in tree structures, snowflakes, and some leaf patterns. For example, the photo to the right shows a plant that has fractals in its leaves. It is amazing the amount of geometry that can be found just outside in your backyards. By providing students with examples of places geometry can be found in nature, they will start to notice all the mathematics that is around them.

Retrieved from: http://www.pbs.org/wgbh/nova

/physics/mandelbrot-fractal.html

Before I went to the arboretum, I completed a little research on my own and found some interesting ways geometry is found in nature through fractals.  Benoit Mandelbrot, the founder of fractals has many extensive interviews online detailing the importance of fractals and why it is essential to understand it in geometry. In a particular interview that I read from 2008, Mandelbrot emphasized how natural structures are not perfect shapes. For example, clouds do not have smooth sides, rather they are rough, and that is why fractals are important to understand.

An activity that teachers could have their students complete in the classroom is Fractals in High School: Exploring a New Geometry by, Randi Lornell and Judy Westerberg. This activity had students complete hands-on activities that led them to discover what fractal geometry was. This article gave four mini activities that could be completed. By integrating activities like these in the classroom, teachers will be having their student explore topics from a new approach. It allows students to make connections to geometry and the nature around them.

 

A second lesson that I found interesting was a lesson from PBS on fractals and the coastline. This lesson had students use fractals to find the length of a coastline. Just like other natural structures, a coastline is not a smooth, straight surface. It has ridges and edges. Therefore, fractals are a great way to investigate the actual length of different coastlines.

Through the integration of geometry and nature, students will be able to see the mathematics in the world around them. By giving students the opportunity to research where geometry is found in nature we are providing them with the chance to relate to the topic. The Dallas Arboretum is a great place to start if you want to get your students minds wondering outside of the classroom.