The Challenge: Crochet your very own Hyperbolic Plane (or Pseudosphere?)
Materials Needed: Crochet hook, yarn.
Math concepts you could explore with this challenge: exponents, hyperbolic geometry, proportions/ratios, topology
You do not need to be particularly good at crochet. If you can crochet the most basic stitches (chain and single crochet), you can make this.
Hyperbolic Crochet is the brain child of Daina Taimina. Please check out her blog here: http://hyperbolic-crochet.blogspot.com/. She’s written a beautiful book: Crocheting Adventures with Hyperbolic Planes that I highly recommend. All of my work below is directly as a result of her.
And if you’re teaching exponentials….
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. What does it look like to draw a straight line on a hyperbolic plane? To draw a triangle? What does it mean to measure an angle? How can you measure distance on the hyperbolic plane?
8.) Look for and express regularity in repeated reasoning. Given the ratio that any hyperbolic plane is created with, make an exponential function to predict the number of stitches in any given row.