I saw Steven Strogatz share a quote from Rota earlier in the week:
This passage both struck me and annoyed me – not totally sure why:
It is certainly not the case that everything that is interesting to mathematicians is going to be interesting to either the general public or to kids learning math. Nonetheless, there are many ideas beyond the (maybe overshared) “usual pap of Klein bottles, chaos, and colored pictures” that are indeed worth sharing.
So my challenge for everyone in math is to write one post – just one post – sharing an idea that shows something that might be interesting to both mathematicians and to students learning math. For every post that gets shared with me, I’ll write another one 🙂
Here’s my first idea. I saw it originally from Ann-Marie Ison and then more recently from Burkard Polster aka “the Mathologer”. The idea shows some fascinating geometry hiding in modular arithmetic.
Our two projects with this type of modular arithmetic are below:
I think the best way to play with the modular arithmetic patterns is via this Desmos activity written by Martin Holtham:
Also, a good way to dive a little deeper into what’s going on in these pictures is this video from Polster:
I used this modular arithmetic idea in lectures at two math camps last year and both times the kids were just blown away. The connection between geometry and arithmetic here is so fun and so surprising that it is hard to imagine anyone seeing it for the first time not being blow away!
So, no gimmicks, no super abstract math, but something that I think would be both enjoyable for students learning math and something that mathematicians will not throw back on the shelf in disgust.
What are some other ideas 🙂