Using Dillon Berger’s tweet about Mars to talk about polar coordinates with my kids

I saw another great tweet from Dillon Berger yesterday:

After seeing it I thought that talking about the orbits of the Earth and Mars would make for a great project with the boys today. We started with some basic ideas and the kids actually had some ideas that related to Kepler’s Laws, which was super fun:

Next we moved to the computer to look at Berger’s tweet and see what he boys had to say about it:

Now we went back to the white board to talk about representing the orbits with polar coordinates. My younger son is just learning about polar coordinates now and I started the conversation here a bit too quickly, I think, but even with the bad start hopefully we had a productive conversation:

Finally, we went back to the computer to look at a simplified program illustrating what the orbit of Mars looks like when viewed from the Earth.

This project was really fun – I’m really grateful that people like Dillon Berger share so many amazing ideas about math and physics on twitter. All of that sharing makes finding fun projects to do with kids so much easier!

Having the boys try out some fun and surprising ideas about 360 and 720 degree rotations from Eric Weinstein’s interview with Roger Penrose

Yesterday I heard a terrific interview with Roger Penrose on Eric Weinstein’s podcast:

The podcast episode is here:

‘Today the boys and I talked through three fun to see, but maybe tricky to understand, ways that something need to rotate 720 degrees to get back to where it started.

We started by looking at a circle rotating around a second circle of the same size:

Next we looked at the famous “wine glass” problem. I originally wanted to color the water in the glass with food coloring, but chickened out!

Before going on to the Dirac Belt Trick, I showed the boys this really nice video showing the trick in a pretty unusual – and super fun – way:

After the video demonstration, I had the boys try the trick with a belt. At the end my old son made a connection between the belt trick and the complex numbers which was a nice and totally out of the blue surprise to me:

Anyone interested in physics should listen to Weinstein’s interview of Penrose – it is amazing. I was really happy to be able to pull out a few ideas from the interview to share with the kids today!

Exploring some of the recent Betelgeuse observations with kids

A lot of people have been talking about recent observations of the star Betelgeuse this week. Here’s one great thread I happened to see:

After seeing this thread I thought it would be fun to share some of the ideas about the recent observations of Betelgeuse with the boys. Although I’m way out of my league here, there were some great resources I found that I thought would help the boys understand what was going on. Two of those resources were:

A discussion on Astroblog about Betelgeuse

The Light Curve Generator from the American Association of Variable Star Observers

I started today’s project by showing the boys the article on Astroblog and then the graph in Eric Mamajek’s tweet:

Next we looked at a graph from the Light Curve generator showing how the brightness of Betelgeuse has varied going back about 6 months. Sorry for the glare on the computer screen 😦

The boys had different ideas about how to interpret the data – which was fun to hear:

Next I had each on my son’s create a new graph. My younger son went first and he wanted to look at the observations from a single astronomer. We did this by using the green dots since there were only to people who collected that data. The astronomer whose data we looked at was Wolfgang Volmann:

My older son went second – he wanted to look at the observations of Betelgeuse going back a long time. We were able to zoom in on a time period in the 70s and 80s in which many observations showed that Betelgeuse was pretty dim.

This was a really fun project to work through with the kids. It really highlights the difficulty of collecting data in astronomy, and in the real world in general! It was fun to hear their ideas about how to think through the

Sharing Ricky Reusser’s ‘Periodic Planar Three-Body Orbits” program with my son

I saw an really neat idea in a tweet from Nalini Joshi yesterday:

A direct link to Ricky Reusser’s incredible 3-body problem visualization is here:

Ricky Reusser’s amazing 3-body problem visualization

For today’s math project I asked my son to play around with the program and pick three examples that he found interesting. The discussion of those three examples is below.

Here’s the first one, with a short discussion of three body problem at the start:

Next up was an orbit shaped almost like an infinity symbol:

Finally, an orbit that it completely amazing – I almost can’t believe a shape like this is possible!

Sharing a new “picture” of the Milky Way with kids

I saw a new image of the Milky Way last week thanks to these two tweets:

After seeing the first tweet from Kayley Brauer I was hoping to find a way to talk about this new result with the boys, but didn’t really know what to do. Thanks to the tweet from Dr. Chanda Prescod-Weinstein, I learned that the LA Times had put together a terrific presentation that was accessible to kids.

First, I had my older son read the article on his own and then we talked through some of the ideas he had after reading it.

I thought that reading the article on his own would be a little too difficult for my younger son (he’s about to start 8th grade) so instead of having him read it on his own, we went through it together:

Obviously I’m not within 1 billion miles of being an expert on anything related to this new image of the Milky Way, but it was still really fun to talk about it with the boys. I’m very happy that advanced science projects like this one are being shared in ways that kids can see and experience.

Trying an experiment described in Steven Strogatz’s Infinite Powers with my son

I got my copy of Steven Strogatz’s new book back in April:

I’ve used it for two projects with my kids already:

Using Steven Strogatz’s Infinite Powers with a 7th grader

Following up on our conversation about Steven Strogatz’s Infinite Powers with some basic calculus ideas

Today my older son was back from camp and I thought it would be fun to try an experiment that is described in the first part of chapter 3 of the book. The experiment involves a ball rolling down a ramp and is based on an experiment of Galileo’s that Strogatz describes.

I started by having my son read the first part of chapter 3 and then tell me what he learned:

Now we took a shot at measuring the time it takes for the ball to roll down the ramp.

I misspoke in this video – we’ll be taking the measurement of the distance the ball travels after 1 second and then after 2 seconds. I’m not sure what made me think we needed to measure it at 4 seconds.

Anyway, here’s the set up and the 5 rolls we used to measure the distance after 1 second.

Here’s the measurement of the distance the ball rolled after 2 seconds. We were expecting the ratio of the distances to be 4 to 1. Unfortunately we found that the ratio was closer to 2 to 1.

We guessed (or maybe hoped!) that the problem in the last two videos was that the ramp wasn’t steep enough. So, we raised the ramp a bit and this time we did find that the distances traveled after two seconds was roughly 4 times the distance traveled after 1 second.

This is definitely a fun experiment to try out with kids. Also a nice lesson that physics experiments can be pretty hard for math people to get right πŸ™‚

A project for kids inspired by the Mathematical Objects Podcast

[sorry for mistakes – this one was written up in a big hurry]

I’m a big fan of the Mathematical Objects Podcast hosted by Katie Steckles and Peter Rowlett. Their most recent episode talked about Newton’s law of cooling and I thought it would be fun to try the project at home. Here’s link to the specific podcast:

Note that this project does require some adult supervision because it involves boiling water.

The idea in this project is to explore Newton’s law of cooling two different ways. The first way is to talk about the law, observe some water cooling for a bit, and then make a prediction about how that cooling will proceed. The second way is to take two cups of hot water and compare the temperature when you add cold milk to one initially and to the other 10 min later.

Here’s how we got started:

Next we took two glasses of hot water and measured the initial temperature:

5 min later we returned to measure the new temperatures and then use Newton’s law of cooling to predict the temps 5 min later. This part of the project was a little hard to do on camera, but you’ll get the idea of the things you have to keep track of. Hopefully we did all of the calculations right!

Next we moved on to the “tea” experiment. Here we started with two cups of hot water and added milk to one of them. We are going to wait 10 min and then add milk to the other glass and compare the temperatures of the two cups. Both kids mad a prediction about what would happen:

Finally, we returned to the cups and finished the 2nd experiment. Both kids guessed right on the relative temperatures, but I’m not 100% sure that we got the amount of water and milk exactly equal in the two cups. Still a fun experiment, though.