Saw this tweet from the American Mathematical Society yesterday:

It was such a neat article and I wanted to try to share some of the ideas with my kids today. They are heading into 4th and 6th grade and *obviously* are not experts in topology – ha! It was super fun to hear their ideas as we explored the shapes in Lamb’s article, though.

We started with the classic coffee cup and doughnut example. Their ideas about how the two objects could be the same are absolutely fascinating. It would be amazing to hear how a room full of kids would think about the similarities!

Next we moved on to talking about the infinite earring. Here, too, they have some fascinating ideas about this shape. Among their ideas is that you can keep blowing up the shape so that the smaller circles become equal to the original large circle, but the shape somehow stays somewhat the same.

Near the end of this video I introduce the idea of drawing a small circle around a couple of different points on our shape and then asked the kids what they thought was going on.

When I turned the camera off at the end of the last video it fell off the tripod and crashed down onto the table. It was probably a small miracle that it didn’t break – it sure sounded like it did ðŸ˜¦ Anyway, after that excitement we picked up on where we left off in the last video.

What is special about these extra little circles that we drew? The kids don’t see the shape the same way at first, but eventually they come to an agreement on what is going on. Once again, it was really fun to hear their ideas.

The next shape we looked at was Evelyn Lamb’s “even more infinite earring.” Is this shape the same as the shape we looked at before, or is it different?

My older son’s initial thought is that if you blow up the first shape so that the largest circle now has a radius of infinity you’ll get this shape.

My younger son finds a potentially interesting hole in that argument – this is why I love hearing kids talk about math ðŸ™‚

Eventually we return to the small circle idea in the last video and the boys are able to understand how this new shape differs from the prior one.

Such a fun project to do with kids. A million thanks to Evelyn Lamb for her amazing article!