Day: August 28, 2016

Building Solar Cars thanks to Megan Hayes-Golding

Saw this tweet last week and, despite my technical skills being in the micro-Hayes-Golding range, I just had to try it!

We ordered the cars from Kelvin LP:

Kelvin LP’s Solar Car

and started building the cars when they arrived on Friday. Here’s what the boys thought at the beginning of the project. My younger son first:

and then my older son:

We built for about 45 min and got about 1/2 way there. The building is not that challenging, though I’d guess our 45 minutes with a 5th and 7th grader would be closer to 15 min with high school kids.

Here’s where we got to after the work on Friday night (the main tools that you need for the build are a glue gun and a soldering iron) :

After about another 30 min of building this morning we’d finished the cars. We used some spare lego pieces to help the solar panels tilt up.

Our first test out in the street didn’t go as well as I was hoping because it was a little cloudy, but at least the wheels still ran and the boys seemed pretty happy:

Later in the morning, though, we got enough sun on our porch to do a nice demonstration:

So, not really a math project but still really fun. Thanks to Megan Hayes-Golding for this great idea!

A talk I’d love to give to Calc students

I saw a neat video from Gary Rubenstein recently:

In the video he presents a neat Theorem about partitions due to Euler.

Simon Gregg, by coincidence, was looking at partitions recently, too, and has written up a nice post which includes some ideas from Rubenstein’s video:

The part that struck me in Rubenstein’s video wasn’t about partitions, though, it was about the manipulation of the infinite product. It all works out just fine, which is pretty neat, but sometimes manipulating infinite quantities produces strange results. See this famous video from Numberphile, for example:

Just as an aside, here’s a longer and more detailed explanation of the same result:

The fascinating thing to me is that Euler’s proof in Rubenstein’s video is easy to believe, but the sum in the Numberphile video is not easy to believe at all. Both are examples, I think, of what Jordan Ellenberg called “algebraic intimidation” in his book How not to be Wrong. I used Ellenberg’s idea when I talked about the -1/12 sum with my kids:

Jordan Ellenberg’s “Algebraic Intimidation”

The talk I’d like to give to calculus students would start with the theorem presented in Rubenstein’s video. Once the students were comfortable with the ideas about the infinite products and the ideas about partitions, I’d move on to the idea in the Numberphile video. It would be a fun way to show students that infinite sums and products can be strange and you can sometimes stumble on really strange results.