Week 37: Cantor Set Kirigami

For this week’s activity, learners can play with Cantor Set Kirigami. The Cantor Set is created by drawing a line. Next, remove the middle third of that line (this will create 2 lines). For each of the two lines just created, remove the middle third (this will create 4 lines). Continue with this process until the lines are too thin to work with.

Menger Lux Blox

Some of the fun characteristics to notice is the pattern of the line lengths (1, 1/3, 1/9, 1/27,…), the number of lines generated with each iteration (1, 2, 4, 8, 16, …), the fact that this set is infinite, yet not countable and that it gets smaller and smaller with each iteration.

I created a fun Kirigami Cantor Set and have the template below with a video how-to. Enjoy!

Learners can also draw Cantor Set cities, roads, abstract art, and find many ways to represent this simple fractal. The Menger Sponge is one form of a Cantor set in 3d.

If you need a jpg. of the sheet:

Week 35: Yarn-it-up Hyperbolic Space

This week let’s play with yarn! We are going to play with hyperbolic space. You will need some yarn and a crochet hook. You don’t need to know how to crochet, but you will need a little patience and a lot of desire to play. These don’t have to be perfect, and “mistakes” just add to their beauty. There is a great TED Talk on crochet coral that is a great intro into this activity as well (click here), or just watch the videos I put together below. I thought about drawing hyperbolic space as an activity, but decided that having the tactile fluffy math in hands would be much more exciting this week:

Week 24: Pastel Diagrams and Plots

Hyperbolic Paraboloid

Sometimes math diagrams, plots, and examples can be a little dry in our books and on the board. This week learners will be taking a diagram or plot that they want to improve upon and sketch it up with pastels, paints, or other media. Color, composition, and artistic embellishments can be added while, keeping the overall concept in tact. Ask them what a math textbook would look like if they created it. Would you have a cheshire kitty in the mix? Would you turn each chapter in to a different land or island?

These sketches don’t have to be fancy, I recommend small pieces of paper and having fun with it (most of these are around 3×5 inches and took a few minutes.) Most of all – have fun!

Binary, powers of two, exponential…
D6, cube, hexahedron, volume, probability…

Week 10: Power of Two Tag

Tag is a great way to get moving, and it isn’t just for kids. I have had my highschool groups play with just as much zeal as the 5 year olds. For this week I encourage learners to create outdoor tag games that incorporate a mathematical concept.

Here is an example using the power of 2 in tag:

  • Start of tag – 1 person is “it”
  • That person has to tag 2 people to become “not it”
  • Now two people are “it” and they must tag 2 people to become “not it”
  • The game ends when everyone is “it”

With chalk learners can draw an “it” tree to show the exponential growth of the game (1,2,4,8,16,32… or 2^0, 2^1, 2^2, 2^3, 2^4,…)

Kitty in a Binary Tree

If you must translate, then here it is:

01010100 01101111 00100000 01100011 01100001 01110100 01101110 01100001 01110000 00100000 01101111 01110010 00100000 01101110 01101111 01110100 00100000 01110100 01101111 00100000 01100011 01100001 01110100 01101110 01100001 01110000 00111111 00100000 01010100 01101000 01100001 01110100 00100000 01101001 01110011 00100000 01110100 01101000 01100101 00100000 01110001 01110101 01100101 01110011 01110100 01101001 01101111 01101110 00101110