#MathArtChallenge Day 8: Apollonian Gaskets

The Challenge: Draw a large shape. Then place a large circle inside that shape, touching at least one edge of the original shape. Then draw the next largest circle you can, and repeat drawing the next largest circle you can. (See video below for examples.)

Materials Needed: Writing utensil, paper.
Math concepts you could explore with this challenge: : Ratios, radius, tangency (tangent circles), proportions, area, perimeter, fractals, geometry

If you’re interested in some of the math behind this, this is a great article, featuring the work of mathematician Hee Oh.

Vi Hart also has a great video along these lines, demonstrating some serious doodle skills.

Depending on how you use this activity, you may engage with different mathematical standards. I’ve listed possible connected math content above. Here are a few suggestions for how you might integrate the 8 mathematical practices. Feel free to add your own suggestions in the comments!

5.) Use appropriate tools strategically. What tools make this easier or more difficult? Is it necessary or better to use a compass and be completely precise, or is it better to “eye-ball” it?

7.) Look for and make use of structure. How does the radius of the largest inner circle affect the radii of the other circles?

8.) Look for and express regularity in repeated reasoning Compare multiple drawings. How does the choice of largest inner circle affect the final outcome? The amount of positive to negative area?

Author: Ms. P

Math Teacher in Minneapolis, MN.

8 thoughts on “#MathArtChallenge Day 8: Apollonian Gaskets”

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