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!

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

Week 23: Fibonacci Weaving

If I am not playing with math, then I am tangled in yarn and thinking about math. This week I combined the two and wove A small fibonacci washcloth. Fiber arts are so versatile and an insanely fun way to express mathematics. In future weeks we will look at collage (wool applique), Cantor art, etc.

Fibonacci is a sequence where you start with 0 and 1. You then add those to get 1: {0,1,1}, and then you add 1 and 1 to get 2: {0,1,1,2}, and then you keep adding the last two numbers to get the next number. Here is a comic I created for Marie’s Atlas on Fibonacci:

For weaving, you need a piece of cardboard, small loom or even a notebook card (for thread weaving). The idea here is to create any form of Fibonacci patterns in your work. For mine I did 8 for a lower border, then 1 blue, 1 white, 1 blue, 1 white, 2 blue, 2 white, 3 blue, 3 white, and so on. Below is a sample. There are tons of ways to weave this sequence. You can use different sized looms, patchwork squares with areas that equal the sequence, etc. Have fun!

Week 22: Tessellations – Paper Method

This week we will do tessellations that fit together through translation (moving without rotation). We will look at reflection and rotation in other weeks. There are a few different ways to do this, but we will use the paper method today. I always start the class by talking about what different kinds of shapes can tessellate (triangles, trapezoids, hexagons, rectangles, etc.). We look at the tessellations around us (bricks, floor tiles, fabrics, etc.)

If you have never made a tessellation before, the easiest way is to use a rectangle sheet of paper, with a pencil, scissors and tape. Here are the instructions:

  • Step 1: Sketch a curve that stretches from the bottom left to the bottom right corner of your rectangle
  • Step 2: Cut out your curve and move it to the opposite side of your rectangle. Tape it together as perfectly as you can.
  • Step 3: Sketch a curve from the top left of your rectangle to the bottom left.
  • Step 4: Cut out the curve on the left and then tape it to the opposite side (again as perfectly as you can).
  • Step 5: Trace your shape on a sheet of paper and add some fun details: