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2 min read 52 Weeks of Math Activities

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
A toothpick fractal being drawn on graph paper
a close up of the tooth picks on a table making the toothpick fractal
the toothpick fractal made of toothpicks on a table

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:

3 toothpicks of the fractal

And then place toothpicks centered at each end again:

7 toothpicks of the fractal

Repeat this process at the ends that are available:

11 tooth picks of the fractal
15 tooth picks of the fractal

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

a tooth pick gif where the fractal forms, then turns into worms and collapses

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!

A toothpick fractal being drawn on graph paper
a student making a fractal on graph paper

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Sophia

Mathematics educator and creative coder exploring the beauty of mathematical concepts through interactive visualizations and playful learning.

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