#MathArtChallenge Day 56: Hyperbolic Crochet (all credit to Daina Taimina)

The Challenge: Crochet your very own Hyperbolic Plane (or Pseudosphere?)

Materials Needed: Crochet hook, yarn.

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….

#MathArtChallenge Day 4: Hyperbolic Geometry

Day4 MAC hyperbolic planes

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: Hyperbolic planes, vertices, opposites, exponential functions, reflections, symmetry

Depending on how you use this activity, you may engage with different standards. 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 with the others?

5.) Use appropriate tools strategically. As you’re folding this, discuss with students what tools make the folding easier or less easy. 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.

#MathArtChallenge Day 1: Tons of triangles

Day1 MAC

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: Angles, vertices, triangles, graph theory, hyperbolic geometry, counting

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 standards. 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?