During this time of increased social distancing, there are some things that I'm doing a lot less of and a lot less often. For example, I rarely drive my car despite the low price of gasoline. Other things I'm doing a lot more of. I've played more board games in the last three weeks than I have in the last year. Another thing I've been doing more of is interacting with people virtually through video meetings and social media. I have really enjoyed taking part, along with my son, in Annie Perkins (@anniek_p) daily Math Art Challenge on Twitter (#mathartchallenge). You can check out the entire list of math art challenges at https://arbitrarilyclose.com/home/. I've also been reading electronic newsletters from Kent Haines (@KentHaines) and Dan Finkel (@MathforLove) on mathematical games and activities for all ages. I recently started reading the weekly Mind-Benders for the Quarantined! from MoMath's puzzle master, Dr. Peter Winkler. There are many talented people creating opportunities and resources for students and teachers to engage with mathematics in new ways.
A recent Math Art Challenge from Annie Perkins made me think about how curiosity can sometimes lead to some amazing connections. It also highlighted for me how having a breadth of experiences and depth of mathematical knowledge can help me pause and notice these connections.
I did this challenge with my son. He got frustrated with this challenge in that his circles were not exact (he is 8 years old). I started to show him how to use a compass to make the circles. We worked on it for a while together. He moved on to another project and I finished by adding a bit of color.
Later, I was reading the Games for Young Minds newsletter in which Kent Haines suggested Sierpinski triangles as a math project for kids that helps reveal the beauty of mathematics. I noticed the connection here between Annie's art project with Apollonian Gaskets and Kent's suggestion of Sierpinski Triangles and then started thinking about all of the other ways that this simple art project might connect to a host of different mathematical ideas.
Here is a short list of some of the related connections that I saw or explored after doing this project:
I notice that many of these topics are not explicitly in the mathematics curriculum. That being said many of them can be a way to look at curriculum outcomes from a different perspective or as a way to practice fundamental skills. What other things come to your mind when exploring this activity? When have you discovered unexpected mathematical connections when exploring a new activity?