Yesterday (after a few false starts!) I printed several different versions of the torus in different L^p metrics. Here they are next to spheres in the corresponding metric
The idea was inspired by an old project that was inspired by a Kelsey Houston-Edwards video
Sharing Kelsey Houston-Edwards’s Pi video with kids
Prior to the prints finishing I talked through some of the shapes as they appeared on the computer with my younger son:
Exploring different L^p versions of the torus
When the various torus prints were done I asked each of the boys to tell me what they thought about the shapes. I love how 3d printing allows you to share advanced ideas about math with kids so easily!
Here’s what my younger son had to say:
Here’s what my younger son had to say:
These are the kinds of math conversations that I’d like to have with kids.
Mike's Math Page 