#MathArtChallenge Day 13: Overlapping Circles

The Challenge: Can you figure out all of the ways that 3 circles can overlap and intersect with each other?

Materials Needed: Curiosity and patience. Whatever medium you like! Please watch ONLY the first 1 minute and 20 seconds of the video below. If you watch more, the answer will be given away! Don’t ruin it for yourself! It’ll be so satisfying if you do it yourself!
Math concepts you could explore with this challenge: circles, combinatorics & permutations, vertices/intersections, radii

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!

1.) Make sense of problems and persevere in solving them. This one really does require perseverance. And constant critique of your current methods.

2.) Reason abstractly and quantitatively. What is the minimum number of intersections? What about the maximum? How can that help you narrow the possible arrangements you need to investigate?

7.) Look for and make use of structure. Can you identify different repeatable structures to help you in this problem? The problem is simple to understand on the surface, but wildly complex when you engage.