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. Can we guess?

    Because I reckon I know what you’re after, and I know you generally encourage people to put their cards on the tabe & get invested in a question.

    But there’s always the chance that discussing your purpose would influence the rectangles people draw, so… yeah, I’m asking for permission first.

  2. we had some students doing a very similiar experiment. i wonder if you are trying to achieve a similiar result. i will also wait until permission to guess what it is your looking for

  3. I did this with my students this morning; I can send you the results if you want. They were, for me, unsurprising; but the set-up (“This is what I did with other math teachers this weekend!”) was worth it. My students are still in suspense.

  4. My guess is…

    You’re trying to figure out the goldilocks rectangle, not too wide, but not too squareish, in an effort to discover something phi-nominal. Phi-l free to delete this if you think it will skew the results… If its not what your going for, i’d like to borrow your data cause i thought of a similar experiment a few days ago but didn’t know how to pull it off.

  5. How come one can only draw rectangles that are aligend with the screen ? Why can’t you do a rectangle which is at a different orientation?

  6. I had kids draw, then measure (in cm) then calculate the ratios. It only took about 5 minutes total for each class.

  7. Hi,
    I did it. But, I would like to point out that I just clicked on a suspicious link which is something that I spend a lot of time teaching students NOT to do.

    It’s only because I’ve read you for awhile that I did it. Please be sure to include some education, at the reveal, about the risks inherent in clicking on unidentifiable content.

  8. I resisted the urge to try and skew the results by making a really ‘skinny’ rectangle off to one side. :)

    Another interesting experiment would be to get people to draw a right triangle.

    I posit that a majority would be similar to this:


    with the longer leg on the bottom. (I hope the spacing in this post is preserved.)

  9. Since you didn’t prohibit guesses, I guess this is an attempt to show that the average dimensions of what people consider a rectangle will show to be extremely close to a 1.618:1 (golden) ratio.

  10. Dave:
    No complaints on my end :)
    It really is only relevant based on question you (as a teacher/researcher) are trying to answer.
    For example – if you wanted to know what is the typical (or prototypical) rectangle, then by limiting the drawing to only “screen-aligend” lines, you are missing an opportunity to see if students consider other orientations as rectangular (which is actually a known problem that students do not identify rectangles of that kind).

    But, as I said – I don’t know what they goal of this was, so maybe the design is suitable.

  11. I’m getting an error message that starts like this:

    Errno::ENOENT in Rects#index

    Showing /var/www/railsapps/rectangle/app/views/layouts/application.html.erb where line #5 raised:
    No such file or directory – /var/www/railsapps/rectangle/tmp/cache/assets/sprockets%2Fd585a06e2ee6203ccb04c8b84150d14d20121023-32745-ewt05k.lock

  12. I wonder how many people draw a square, just to be different?

    I’m wondering how much the interface affects answers. I clicked twice intending to get something more rectangular but eyeballed wrong so it ended up square-ish, and rather than bothering with changing around my answer I just hit send.

    Fun to note: there are places in the world that still follow original Euclid so that a square is not a type of rectangle. Would people from those locations shy away from the square-like rectangles more?

    Bizarre to note: In Wales “squares” and “diamonds” (tilted squares, not rhombuses) are two different things.

  13. “Bizarre to note: In Wales “squares” and “diamonds” (tilted squares, not rhombuses) are two different things.”

    Reminds me of when I talk to students about oblongs. ‘That’s a rectangle’, they cry. ‘Actually it’s a rectangle that’s not square’, I respond. Much puzzlement ensues!

  14. a different Dave

    October 24, 2012 - 8:35 am -

    I predict that the shape of the rectangles is going to be very heavily influenced by the shape of the canvas provided.