Week 39: Toothpicks

A box of toothpicks can lead to an afternoon of entertainment. This week learners can play with the toothpick sequence. The sequence produces really interesting geometries and lines as it grows. I recommend watching Numberphile’s Youtube video on this sequence here. There is also OEIS’ website that allows for play with variations and many iterations. Grab a box of toothpicks and let’s begin:

Start by placing a single toothpick:

And then place toothpicks centered at each end:

And then place toothpicks centered at each end again:

Repeat this process at the ends that are available:

I also made a GIF in Procreate (stop animation is a wonderful way to play with all sorts of math):

Allow for play with the toothpicks to see what other mathematical patterns and tessellations are created.

Another option is to use graph paper to draw this sequence. Have fun!