#MathArtChallenge Day 1: Tons of triangles

Day1 MAC
A sketch of many connected triangles, 7 per vertex. The triangles radiate out from the center, and begin bunching together at the edges as they’re no more space for the growing number of triangles.

The Challenge: Draw as many connected triangles as you can. Goal is to have as many vertices with 7 triangles as possible.

Materials Required: Writing surface, writing utensil
Math concepts you could explore with this challenge: angles, counting, exponents, fractals, functions (exponential), triangles, geometry, graph theory, hyperbolic geometry, lines, polygons, sequences, intersections/vertices

Here’s a quick video tutorial after lots of requests for help in the comments.

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 are best for this activity? How might your materials (sharpie vs fine tip pencil) change your level of success?

6.) Attend to precision. Mistakes will happen (6 lines or 8 rather than 7) when creating these. How can you minimize them, and what planning can you implement to minimize them?

7.) Look for and make use of structure. Is there a “best way” to grow this? How is your success altered when you alter the length of the lines?

Author: Ms. P

Math Teacher in Minneapolis, MN.

47 thoughts on “#MathArtChallenge Day 1: Tons of triangles”

    1. Start with a vertex (point, dot, as you like). From that dot, draw 7 lines coming off of it. Connect the ends of each of those lines to make triangles. Every time you have 2 or more lines meet, that’s a new vertex. To get this specific type of design, you want to try to make all vertices have 7 lines (edges), and to always make triangles when you can. There’s a nice (slower!) tutorial in this video: https://www.youtube.com/watch?v=xu-RSUGBgpA


    1. because math is visual and is more art than science. This is about geometry and spatial sense and, proportionality among other things. Math isn’t just about operations my friend. This is a great task!


  1. Questions for my students: I wonder if it would be easier to draw 3 triangles around each vertex instead? or 4 triangles around each vertex? 5? 6? 8?


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