#MathArtChallenge: Day 2 Looping Colors

Day2 MAC
A looping line, with created spaces alternating blue and red in color.

The Challenge: Draw a long, looping, self-intersecting line that meets back with itself at the start. Avoid having any 3 lines cross at the same intersection (although after a bit it may be fun to play with this). Then, select a color, and start coloring in the spaces created by your line’s intersections.
Can you color it such that you end with every section alternating colors?

Materials Needed: writing utensil, writing surface
Math concepts you could explore with this challenge:
counting, functions, geometry, knot theory, vertices/intersections

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. Can every graph be 2 colored? As you add intersections, how many new spaces are created? Can you create a function to describe the relationship between the number of intersections and the number of enclosed spaces?
2.) Reason abstractly and quantitatively. How many new spaces does each crossing create?
6.) Attend to precision. Ensure that a 2-coloring is correct by methodically working through your design.

Author: Ms. P

Math Teacher in Minneapolis, MN.

47 thoughts on “#MathArtChallenge: Day 2 Looping Colors”

    1. This has been my go-to doodle for 50+ years. I did this to a motorcycle helmet with 1/4 inch masking tape, and sprayed on the second color. (silver on black) One of a kind. Wish I still had it.

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  1. Rules of the Game:
    1) Do not pick up your pencil when you are drawing the looping doodle.
    2) You must end where you begin.
    3) Spaces that share a boundary must be different colors.
    4) Spaces that share a point are allowed to be the same color.

    Questions for my students:
    Can you draw a doodle that requires MORE than 2 colors?
    What if you are allowed to lift your pencil when you draw the doodle? Now can you draw one that requires more colors?
    How many colors does it take to color in a map of the US?
    Can you draw any doodle that requires MORE than 4 colors?

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    1. Sorry about that. I recently updated the post and must have lost the instructions in the shuffle. I re-added them now.

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  2. hi I really like your artwork, it looks really neat and well done.it just didn’t work out for me well I don’t get the instructions maybe if there was a full video tutorial I would understand the instructions .i did try my best thought

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    1. Is it will be more difficult if you use 3 colors in this case? there may have some cases the color of nearby area is the same. I guess

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