#MathArtChallenge Day 4: Hyperbolic Geometry

The Challenge: Fold your very own Hyperbolic Plane from a simple piece of paper!

Materials Needed: A square piece of paper. Youtube instructional video below!
Math concepts you could explore with this challenge:  Algebra (how many folds per stage?), angles, counting, exponents, functions, geometry, Hyperbolic planes, proportions/ratios, sequences, symmetry, topology, 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!

4.) Model with mathematics Compare this model to a surface with positive curvature (a ball) or zero curvature (a piece of paper) surfaces. This surface has negative curvature. What do you notice about the 3 types of curvature? What’s the same? What’s different? What can you do on this surface that you can/cannot do on the others?

5.) Use appropriate tools strategically. As you’re folding, discuss with students what tools make the folding easier or more challenging. What kinds of paper works best? What sizes?

6.) Attend to precision. Discuss with students how successful your models are depending on the precision of your folds.