I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. As I was watching this I kept on checking myself to see if I had any questions, but I wasn’t finding myself particularly pained by any of them (how periodic is his swinging? how long is the period?)

    If instead of height from the ground we were plotting distance from the middle, maybe we could have somebody running from far away at a constant speed towards the middle of your swing. I think then there would be a pretty irresistible question that could be solved as a system of a linear-trigonometric equations.

  2. Alex Eckert

    May 16, 2011 - 7:07 pm -

    I’d love to see a video tutorial explaining the programs used to create this. In particular, when you show the answer, what do you use to graph the curve?

  3. Wicked cool, especially the last six seconds. A lot of kids just “stop” the graph at a point when that sort of thing happens. I have used this example with my kids but only as thought experiment. What do people think about offering the thought experiment version to kids first, then the video version a few minutes later?

    I always had the impression that this kind of pendulum swing wasn’t a true sinusoid in the height function — that you spent more time at a low height than at the peaks. Looking more carefully, it appears the graph drawn in this video isn’t a true sinusoid but for a different reason: when you’re pushing forward there is less time taken on the downswing because velocity is higher.

    So I’d be really curious for a super slo-mo “zoomed in” version for the first 4 or 5 seconds of this thing…

  4. Thanks for that video. It would be great to have a version of your video with metric scale (e.g. in centimeters) on the y-axis.

  5. Are you using After Effects for the animations? Cause it looks great. I keep telling myself I need to get it but the price and the learning curve have kept me at bay. Any thoughts on the learning curve?

  6. Just some thoughts :-)

    – If you plotted the horizontal distance from where you’re going to land over time, how would that look?

    – Speed of swing over time?

    – Distance of head over time? Feet over time?

  7. @Matt & Alex, yeah, that’s AfterEffects right there. The price is worse than the learning curve, which is also kind of annoying. I can’t imagine working without it, though. Alex, I reckon I’ll tutorialize this at some point soon.

    @Jim, you’ve nailed what’s so freaking rich about these videos. You tweak the y-axis even slightly and you get a mind-bending new problem from a context the students already know.

    @Bowen, going in, I was aware this wasn’t a sinusoid, true or otherwise. I may not have represented that well, though.

  8. cheesemonkeysf

    May 17, 2011 - 1:18 pm -

    My students went nuts for these videos this year. I’m excited to have a new one (or maybe more) to add to the mix for next year. Thank you!

    – Elizabeth (aka @cheesemonkeysf on Twitter)

  9. A couple of points:

    1. very professional looking.

    2. You are not a spring chicken anymore. You have to be careful jumping out of these swings. Nothing sucks more than a broken ankle. Well, maybe two broken ankles sucks more.

    3. I love how you look around after you jumped. Did anybody see that?

    4. I might have to use this video in my “how does a swing work” project if I ever get around to it.