The challenge: Create a Hilbert curve.
Materials needed: Paper and pencil. Grid paper is helpful.
Math concepts you could explore with this challenge: exponents, fractals, geometry, sequences, symmetry, tessellations
And here’s a neat extension from Vincent Panteloni:
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!
6.) Attend to precision. Describe, in detail, how to create the next iteration of a Hilbert Curve.
7.) Look for and make use of structure. Why do you think the Hilbert curve is described as a “space filling” curve?
8.) Look for and express regularity in repeated reasoning. How many line segments are necessary for each iteration of the Hilbert?