#MathArtChallenge Day 60: Triangle Incenters ala Matt Henderson

The Challenge: Create your own version of Matt Henderson’s triangle incenters.

Materials needed: Paper? Pencil? Origami? Graphing software? (There are lots of options here.)
Math concepts you could explore with this challenge: angles, geometry, polygons, symmetry, vertices/intersections

find the incenter of a triangle by drawing its angle bisectors. this creates 6 new triangles. repeat pic.twitter.com/vfWATnPKS8

— Matt Henderson (@matthen2) May 16, 2020

I decided the easiest way to re-create this was by folding it – as folding angle bisectors is a fairly doable and learnable task.

There are clearly some mistakes that I’d like to go back and explore later, but this was a wonderful folding puzzle for me. #mathartchallenge pic.twitter.com/D2856iMCId

— Annie Perkins (@anniek_p) May 16, 2020

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! 

2.) Reason abstractly and quantitatively. What can you say, generally, about the any iteration? What can you say about the relative size of any randomly selected triangle in any particular iteration?

5.) Use appropriate tools strategically. What tools make this most successful for you? Is it better to measure, fold, draw…? Why do your chosen tools work well or poorly.