The museum of math has put together a nice (and growing!) collection of videos of mathematicians talking about beautiful math:
Watching the videos it struck me that they were aimed at adults and older kids, but I thought it would be easy to show some beautiful math that younger kids could appreciate, too. I thought of two of my favorite projects with the boys and then asked each of them to tell me what they thought was the most beautiful math that they’d seen.
My two favorites:
(1) The Chaos game:
Our project is here:
Computer Math and the Chaos Game
and my favorite part starts about 2:30 into this video and goes for about 45 seconds:
(2) John Conway’s “Amusical” version of the Collatz Conjecture
Our project is here:
The Collatz Conjecture and John Conway’s “Amusical” Variation
and my favorite part is at the end where we convert the “amusical” process to music. The music starts around 2:00 – prior to that is just explaining Conway’s Collatz process in the Mathematica code. I love it when my younger son says “I didn’t know you could hear 20”:
(3) My older son’s choice for beautiful math – the 4th dimension
We’ve done a couple of projects related to the 4th dimension – here are a few:
Carl Sagan on the 4th Dimension
which had a fun connection to our Zometool / bubble project. Around 1:00 in the video is a great moment – “who knew that bubbles could find the center of a tetrahedron?”
That comment from my son led to this wonderful drawing posted on twitter:
Another really fun higher dimensional problem for kids who know the Pythagorean Theorem is a neat problem I learned from Bjorn Poonen:
Talking through Bjorn Poonen’s N-dimensional Sphere Problem with kids
(4) My younger son told me that he thought fractals were the most beautiful math that he’d seen.
We’ve done several fractal projects for kids, too. Here are a few:
A fun fractal project – exploring the Gosper curve
After this projects, were really luck to receive some laser cut Gosper curves from Dan Anderson to play with:
Using the Koch Snowflake to introduce fractals
Using Matt Parker’s Menger Sponge video to talk fractions with kids
One of my favorite moments from these projects happens around 3:00 in the video below as the boys stretch out a 3d printed Peano curve into (nearly) a straight line:
So, I’m really happy to see the Museum of math putting together a collection of mathematicians talking about beautiful math. I can’t wait to see more videos in the collection! Hopefully some of the videos and projects above can help younger kids see some beautiful ideas in math, too.
Mike's Math Page 