The Beauty of Math
By Leslie Morrison, CTD Summer Leapfrog Coordinator
“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” – Benoit Mendelbrot, 1983
Mathematics is like art, because it helps us see the world in a new way. Fractals point us to the patterns in nature that the untrained eye may not notice.
Prior to the 1970s, geometry was seen as a domain of order. In classical Euclidian mathematics, the math was formulaic and predictable. Straight lines, angles, and triangles dominated, while patterns in nature were seen as irregular and chaotic, outside of classical mathematics. In the 1970s, however, a mathematician named Benoit Mendelbrot introduced a different way of defining geometry. Through fractals, Mendelbrot was able to describe in mathematical terms the infinitely complex repeating patterns in nature, geometry, and algebra. In a fractal, you can zoom in and find the same shapes over and over again, and your search would never end. In the past, humans saw these patterns in nature, but didn’t recognize them in a mathematical way.
A special kind of fractal, call the Koch Curve, showed that in a curved fractal, the length of the curve gets longer and longer, eventually becoming impossible to measure. Fractals are a paradox because they appear to be finite, but they are actually mathematically infinite. Fractals make abstract mathematical concepts visible. They point to a concrete beauty grounded in math, an awe-inspiring way to think of our coastlines, of branches on trees, and the spiraling of the galaxy.
Check out the Fractal Foundation’s Fractivity page for hands-on activities to engage kids in the beauty of math!
This Summer, students will explore the art of math in CTD’s Geometry Doodle class, for grades 2-3 >
Resources
The Nature of Code
http://natureofcode.com/book/chapter-8-fractals/
Fractal Foundation: What are fractals?
http://fractalfoundation.org/resources/what-are-fractals/
Mathematical Monsters
https://orderinchoas.wordpress.com/2013/02/15/mathematical-monsters/
NGS Recursion
http://phenomena.nationalgeographic.com/2014/08/12/to-infinity-and-beyond/
Fractals and Fractal Dimension
http://www.vanderbilt.edu/AnS/psychology/cogsci/chaos/workshop/Fractals.html
Nurturing Mathematical Talent
http://www.ctd.northwestern.edu/spring-2017-talent-newsletter