August 02, 2018

Melinda Contreras

5 Cool Ways to Learn Math Concepts through Art


Are you an art person or a math person? Do you think logically or creatively? We often categorize ourselves based on these questions, but of course being a math person or art person don’t have to be mutually exclusive. Artists often use math concepts like ratios in their work, and mathematicians exercise creativity when they come up with new formulas to solve problems. As much as we love using games to teach math concepts, we also love using art as well! These are some of our favorite visual representations of math!


Musical Fractions

musical-fractionsPhoto courtesy of We Are Teachers

You are likely familiar with the concept of creating music with glasses filled with different amount of water, where each glass produces a different sound when tapped with a pencil. By being precise about the amount of water you pour in each glass, you can turn this activity into a simple introduction to Musical FractionsWe Are Teachers also smartly suggests adding food coloring to each glass of water. By assigning a unique color to each fraction, kids will be able to easily write a color coded melody.



Pi Skyline

pi skyline

Photo courtesy of What Do We Do All Day?

Pi — the ratio of the circumference of a circle to its diameter — has been has been calculated to over one trillion digits beyond its decimal point, though it is known to the average person as 3.14. Though you'll only need the digits 3.14 in most calculations, we love  how What Do We Do All Day? visually represents the many digits of Pi via a Pi Sklyline.

All you’ll need is graph paper, markers, and a printout of Pi with a number of digits equal to the number of buildings you want in your skyline. supplies the first million digits! To complete your skyline, simply color in the number of squares on the graph paper that correspond to each digit of pi, filling in columns of squares for as many digits as you wish. To complete your art, decorate the background in any way you’d like. How long will you make your skyline?

math-art-pi-side-by-sidePhoto courtesy of What Do We Do All Day?





If you’re missing curved spirals and want a more automated way of completing your designs, check out one of ThinkFun’s newest products - the Hypnograph. It’s still in development, but is now available for pre-order on Kickstarter! The Hypnograph allows for massively complex artwork while remaining easy to use. All you have to do is lock in a paper disc, attach one or more gears, place a pen, marker, pencil or crayon, then beginning cranking the handle. In just a few minutes, a beautiful design will emerge!

The Hypnograph machine provides a great way to learn about the greatest common factor between two numbers. By finding the greatest common factor of the turntable, which has 60 teeth, and the teeth on your chosen gear, you will be able to determine how many loops will appear in your design. Our instruction booklet provides a chart of these calculations for your reference!




Fibonacci Art Project


Photo courtesy of What Do We Do All Day?

What Do We Do All Day? posts a lot of projects that combine art and math, and we couldn’t pick just one to share with you. We also recommend this Fibonacci Art Project.  The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. For this activity, Erica recommends using the numbers in your sequence as radii of circles. After using a compass to draw circles of the correct size, cut out each of the circles, then arrange them in any layout you choose. If you’ve mastered fractions (perhaps through musical fractions), you can follow her outline for a sequence of fractions. Otherwise, you can use whole numbers in your calculations (if you don’t want giant circles, use cm as your unit of measure).





Photo courtesy of Eclectic Ed

Hold on to that graph paper and set of markers - they can also be used to explore angles and patterns via Spriolateral designs!

Does the design above look familiar? It might remind you of Spirograph designs, but Spirolateral designs are made of straight lines instead of curves. Eclectic Ed outlines one of the simpler designs to make. The basic rules for Spirolaterals include: 1) Choose an angle to incorporate into your drawing. 2) Choose a set of numbers from 1 through x. 3) Choose a direction to turn each line segment.

To replicate the pattern shown, you first draw a line segment one unit long. Then, make a 90 degree clockwise turn and make the next line segment 2 units long. Turn 90 degrees again, and make the line segment 3 units long. Repeat this process until you make a line segment 9 line units long. After the 9th line segment, repeat the process starting again with a 1 unit line. A closed design will return to its starting point.

To see a wide range of possible designs, check out the interactive tool on The Mathenæum that animates designs using different angles and different sets of line segments.



What are your ways to combine math and art? Share with us in the comments!


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