A terrific problem from Matt Enlow

Saw a fascinating problem and request from Matt Enlow when I was on the road on Thursday:

Everyone always talks about thinking through problem carefully – here’s a great problem and a great opportunity to give some examples of that kind of deep thinking.

Give him some feedback!


Dave Richeson’s Knotted bubbles project

Saw this tweet from Dave Richeson last week which basically “had me at hello”:

here’s the video in cast the twitter link doesn’t work:

We’ve done a few bubble projects in the past, so the boys were already familiar with the basic concept:

Zometool and Minimal Surfaces

Trying out 4 dimensional bubbles

More Zome Bubbles

Anyway, I ran out to home depot and got some wire and we made some knots. I had each of the boys make a trefoil knot and then make a random knot of their own choosing. In retrospect I wish I’d spent maybe just 5 minutes explaining some of the ideas in Richeson’s blog post – oh well, the excitement got the better of me 🙂

Here’s my older son playing with his trefoil knot and making a Mobius strip bubble. I love the “hey, I actually think I got it” moment:

Here’s him playing with the knot me made – in retrospect I’d argue for a knot that was slightly less complicated:

Next up was my younger son. First up was the trefoil knot and we got another great moment “I think this might be a Mobius strip” !!

Finally we made his own knot and explored. Again, I’d probably ask for a less complicated knot if I was doing this again:

So, that so much to Dave Richeson for posting his old project – this is an incredible project, and an especially great one for kids. The appearance of the Mobius strip is really quite an amazing little math miracle!