Project Description

Math and Art

Most people don’t think of math and art as being related, but I regularly find myself using math concepts in my art practice. I use proportions, ratios, and even basic algebra all the time and I think I’m a better artist because of it!

When I am drawing from life, I am very attentive to proportion. I use a string to determine the relationships between parts of the figure to the whole figure. A common example of this is head heights. To figure this out, you stretch your arms out while holding the string and position one thumb on top of the person’s head and the other at the bottom of their chin. From there, you move the string without moving your thumbs to determine how many heads high the figure is. Every person and every pose is different, but I find that 6-7 heads high is typical for a standing pose. Six head heights can be represented as the ratio 1:6. Other parts of the figure can be measured in this same way. This can be used as a way to check one’s drawing for accuracy. When I teach this method, many students are surprised to find how different their initial drawing is from what they are actually seeing!

Measuring head heights

Another way I use proportion is when I am doing a composition study in my sketchbook. I usually work on paper that is 22″ x 30,” so if I make the sketch 7″ high, I would need to figure out what the width would be in a vertical orientation. Figuring this out requires some basic algebra. Here’s how to solve the problem.

Proportion math problem

The basic idea is that with 2 equal fractions, the cross multiples will also be equal. So if I make the width a little over 5 inches, I’ll get an accurate proportion. If you are looking for an easier way, check out this proportion calculator I made.

Composition sketch

Composition sketch
5.13″ x 7″

Work in progress

Work in progress
22″ x 30″

Knowing about proportions is also helpful for making smaller reproductions of your artwork, which many artists do. For example, if your original artwork is 24″ x 30,” you can make a reproduction that is 16″ x 20.” If you try to get a size that is an inch or two off, your image will look stretched out compared to the original.

Those are just some of the ways I use math when doing art. One artist who I always think of as being particularly mathematical is M. C. Escher. His drawings and prints reveal a deep understanding of geometry. In fact, the mathematical concepts he was dealing with in his artwork were ones that mathematicians at the time were also working on. Art can really be as loose or as mathematical as you want to make it!