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The Magic Octagon

One of my favorite moments at NCTM was when I ran into David Masunaga and he showed me the magic octagon.

Take a minute to let the magic octagon blow your mind.

21 Responses to “The Magic Octagon”

  1. on 09 Sep 2013 at 11:50 amDan Allen

    Ha ha, nice. I like this. It would be useful in teaching transformational geometry.

  2. on 09 Sep 2013 at 1:00 pmjosh g.

    This is fantastic.

  3. on 09 Sep 2013 at 4:58 pmsuehellman

    It would be interesting to poll observers on their predictions. I’m going to make one that’s transparent so I can understand the magic.

  4. on 10 Sep 2013 at 3:23 amCathy

    Do I win a prize if I predicted the arrow’s position on the red side correctly each time? Ha!

  5. on 10 Sep 2013 at 4:19 amMatt E

    Wow. Ya got me. And I like to think I’m not east to “get.” Nicely done!

  6. on 10 Sep 2013 at 4:37 amKarl

    Love this! Where do you take the lesson from here?

  7. on 10 Sep 2013 at 4:43 amMichael Paul Goldenberg

    Really great, simple, completely counterintuitive. Love it.

  8. on 10 Sep 2013 at 6:03 amAndrew

    I agree with Dan (comment #1). In fact, we just started discussing rotations and reflections TODAY! How wonderfully timely.

    (and I sympathize with Matt E. It “got” me. In fact, I had to watch the video three times before I figured out what was going on)

  9. on 10 Sep 2013 at 7:48 amCynthia Nicolson

    I’m wondering what mathematical experiences would help make this more intuitive. Playing around with a hexagonal pattern block for a couple of minutes helped me get a feel for it. Does this show the need for concrete as well as virtual materials – even at higher grades?

  10. on 10 Sep 2013 at 10:18 amJames McKee

    I don’t get it. It came out exactly where it was supposed to. What’s the joke?

  11. on 10 Sep 2013 at 11:07 amAndrew

    @James… I don’t think it is a joke, but I was perplexed a bit as to why the arrow didn’t do what I had originally predicted. I had missed that in the way that the octagon was spun at the beginning, it didn’t keep the arrow on the my left side when the back of the octagon.

    So, when I saw that the answer was different than I had predicted, it took me a second to catch up. That’s what I was referring to.

  12. on 10 Sep 2013 at 12:07 pmDan Meyer


    Love this! Where do you take the lesson from here?


  13. on 10 Sep 2013 at 1:21 pmJames McKee

    @Andrew – so most people don’t predict correctly? I guess I can see that. I guess most people would expect the arrow on the back to rotate the “same direction” (clockwise) as the arrow on the front, and don’t see what the reflection is going to do?

  14. on 10 Sep 2013 at 5:31 pmJenny

    I read the comments first so I knew what was going to happen and I still couldn’t wrap my head around it when I watched it. I’m curious now about the differences in the thinking between the handful of folks who knew what would happen and the majority of us who predicted wrong. Any thoughts on the reasons?

  15. on 11 Sep 2013 at 9:04 pmmath teach

    I had to watch it without the sound the second time to “see” it! You were a great magician, distracting me with your words! Great fun….great thinking for the students!

  16. on 14 Sep 2013 at 2:17 pmEric Merryman

    I like this, it is pretty simple, the trick to see past it is to understand that that when side A is at noon, side B without flipping it, is at 3 o’clock, when flipped, it is at the shown 9 o’clock. So when side A is at 2 o’clock, through the paper side B is at 5 o’clock, however when flipped it is at 7 o’clock(how it is shown, due to it being flipped), not the expected 11 o’clock. Side A isn’t flipped, side B is flipped(when shown), so both go in opposite directions.

  17. on 14 Sep 2013 at 10:03 pmBruce James

    I like starting at “12”, like Dan, then going counterclockwise to “11.” That’ll spook ’em!

  18. on 18 Sep 2013 at 11:35 amK.Savage

    These are the kinds of things that I love. When you can get inside their mind, turn it around, and then let the students explore why it works, those lightbulb moments are brilliant. I’m just trying to think if I could use it in a lesson plan early in the year in a 3rd grade class? Possibly what it would tie into/connections to be made?

  19. on 30 Sep 2013 at 5:25 pmThe Magic Octagon | tglennb

    […] See on […]

  20. on 30 Jul 2014 at 7:03 pmEric I.

    I think people are missing the true “magic” of this trick.

    In the first position, as the octagon is rotated, the hands are a 90 degrees apart.

    In the second position, as the octagon is rotated, the hands are 180 degrees apart.

    And then at the third position, as the octagon is rotated, the hands are again 90 degrees apart.

    How can this be?

    To me it’s kind of like this question: How does a mirror know to reverses left and right but not up and down?

  21. on 06 Aug 2014 at 4:17 pmBillie Mitchell

    Amazing. Found you through a TED Talk. I wish we had this perfectly simple way to learn and understand math in my day. Now I am a grandmother to a 3 year old and I hope that this is how we can teach him.