The Challenge: Find a smaller circle you can trace. Then trace large circle to use as a guide. Finally, trace a bunch of smaller circles in a ring to create a torus (more commonly known as a donut).
Materials Needed: Paper, writing utensil(s), circles/compass. The circles can be whatever, but rigid is helpful and even better if they’re empty (masking tape is great!)
Math concepts you could explore with this challenge: circles, geometric construction, proportions/ratios (to get interlocking tori, there are restrictions on the possible ratios between the circles)
Here are mine!
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!
3.) Construct viable arguments and critique the reasoning of others. What kinds of interactions between two tori can be made? What can you deduce about the relative radii of tori that “intersect”?
5.) Use appropriate tools strategically. What tools work best for creating these tori? How might you make an image like this best without a compass? Is there a tool that is actually better than a compass? Why or why not?
7.) Look for and make use of structure. Let’s say you start with a circle of radius 5 units. What’s the largest radius you can use for your circles centered on the torus? What’s the minimum?