There is something about the human brain that finds beauty in symmetry and loves to create order. I experienced this myself when I taught geometry for the first time and learned how to inscribe stars and triangles inside of circles. In hard times, I have repeatedly found that beauty-making soothes my brain. My hope here is to share some relatively easy ways that you and/or your children can experience the benefits of making beauty in the form of geometric shapes.
There are many ways to create interesting and symmetrical shapes — both with and without a computer — and some of them are surprisingly easy to learn. Choose the one that best suits your mind.
A video by Sheldon Collier (“8-Pointed Star Tessellation in Geogebra, Design Two”) can show you how to create an eight-pointed star using the math app Geogebra — learn more here: youtube.com/watch?v=efNLZSa87yw.
There are good reasons to explore GeoGebra… it can help young people learn a lot about geometry and algebra, and many students have fun learning how to use it to create complex, beautiful, symmetrical shapes. But there are also good reasons to learn how to make shapes by hand.
The simplest way to play and create such shapes is by using a spirograph. These interlocking gears have holes that are the same size as a pen point and allow anyone to literally crank out pleasing shapes. At it's more basic, as there is very little art and no math involved in this method of beauty-making but beauty making it is, nonetheless. One challenge is that if your hand is not steady, it is easy to make mistakes; for some people this can be a frustrating experience. A video called "Spirograph Design Basics" by Escape Hatch, is for "anyone who is first getting started with Spirographs." You can watch it here: youtube.com/watch?v=yKCS7KwehQI.
The human mind also finds pleasure in taking something relatively basic and adding to it. To see how Mahesh Pendam uses a spirograph to make ever more complicated and beautiful designs, visit youtube.com/watch?v=qI4IUPpKGJ4 to watch “Spirograph Art Designs." Another great video to check out is one James May made with the BBC called, "Spirograph Artists." I think many adults and children will find it inspires some hope about the extra layers of creativity that are possible.
A third way to create complex, beautifully symmetrical shapes is to use a pencil, a ruler and either a compass or a protractor.
I wish I could find an exciting video about making many-pointed stars within a circle (I tried and failed). When I first learned how to divide up a circle into many equal parts and create a star, I had the same kind of feeling that I had when I first learned how to ride a bicycle as a kid. The videos on the Arthur Geometry channel on YouTube — youtube.com/channel/UCZS2z-KtV2Wb4D95SoTDdKg — lack the tingling excitement of that experience, but they clearly take you through the steps for placing any number of points set equally around a circle using a compass. Once you have opened this door, you can use a ruler to repeatedly connect points in regular patterns. These patterns can produce stars and polygons; Arthur Geometry has a whole series of videos showing how to create them all. I think your brain will quickly grasp many possible ways to create beauty using this technique.
While Arthur Geometry demonstrates how to use a compass to divide up a circle, some minds, including my own, find it easier to use a protractor, which gives the measurement of the angles in a circle. This is the method I personally prefer. And I saved what I think is the easiest method for last, because I know many people skip to the end of an article.
To find where all of the points for a nine-sided star are, first you simply draw a circle using the protractor. The total number of angles in a circle is 360, and we call each one a degree. Why? Visit historytoday.com/history-matters/full-circle to learn why.
To find where you should place each of the nine points, you divide 360 by 9, which equals 40. Start at zero and simply count up by 40 and make a mark at each point. You will have points at 0, 40, 80, 120, 160, 200, 240, 280 and at 320.
To make a star within the circle, start at zero and skip two points until you get to 120. Draw a line segment between 0 and 120, and a second line segment from 0 to 160. If you connect all of the points in the same manner, you will end up with a star. You can layer stars on top of stars, all in the same circle, and play with shading different slivers of stars with different colored pencils, paint or markers.
I hope, dear reader, that you find some time in your day to draw, sing or make a little beauty, no matter how you choose to do so. If you are inspired to use one of the techniques in this article to make beauty, take a picture of it and send it to me at firstname.lastname@example.org. Be sure to include "Order and Beauty" in the subject line.
Rolf Parker, a math tutor, and his wife Cynthia Houghton, an artist, live in southeastern Vermont. To see what they are up, to visit HoughtonArt.com.