Dan Meyer of dy/dan fame has a series of posts titled “What can you do with this?” — where he shows a picture or video with some sort of math connection, and asks teachers how they might use it in class. (Others are jumping on the bandwagon.) I figured why not. I love the idea. What I’ve noticed is that many of the pictures deal with ratios and proportions. I wonder if we can get pictures that deal with other things — like radical equations and limits.
Michael Lugo at God Plays Dice directed me to the following picture:
Fantastic, isn’t it! What you could do in a math class isn’t obvious at first glance. But let’s see what you come up with! For a spoiler (do NOT check it out until you’ve come up with an idea yourself), see below the jump.
This picture comes from this paper.
Continuous Everywhere but Differentiable Nowhere 
I am historically bad at this game, but…
There are neat things going on with the frequencies of the letters creating a curve. I could see how many different curves we could get to fit parts of it, and try to find one that was the closest. And how do we evaluate “close”?
Cool picture! I’m looking forward to hearing what others see in it.
Maybe it’s that so many of us teach ratios for so much of the year that it’s the automatic thought. Certainly was my gut instinct with this one. Thickness of letters number of words that start with that letter.
And I just finished a unit with one class that’s along the lines of the link. Hopefully it’s not to late to pull it out…
Hmmm. A Pareto diagram? (That is, a graph of the cumulative probability distribution that a randomly chosen word begins with a particular letter.)
What percentage of English words come before “pseudo-interesting-example” in the dictionary? (The image gives a geometric approximation method akin to the Pareto diagram; opening the book and finding the page on which “pseudo-interesting-example” [would have] appeared gives an arithmetic approach.)
I suppose one can talk calculus here — where there’s a step function, there’s a Riemann and/or a Lebesgue integral — but that seems a tad far-fetched.
I see a cumulative frequency graph (an ogive). In fact, I think I will steal it for teaching ogives :)
Thanks!