It’s December. My students are nuts. No joke, yesterday I had a student tell me he might throw up. I asked if he needed to see the nurse, was he okay? He said he’d probably be fine, but he probably shouldn’t have eaten soap after his friend dared him. You can’t make this stuff up. We’re all in the long, slow slog to winter break and I feel like I have to pull teeth to get them inspired about math.

On my way home from work I was mulling this over and tried to recall when I was most happy at work recently. It hasn’t been too often. What I came up with had a pretty obvious common element. See if you can spot it.

-I was happy when I asked #mtbos about complex numbers and learned a ton of new-to-me information about what the complex plane is. Sharing that with students who peppered me with incredulous questions and mind-blown expressions was awesome. Loved it.

-I was happy when my geometry class got into a fight over whether 2√2=√8 was true or not.

-I was happy when I saw some students put together that three different quadratic equations were related to the same graph.

-I was happy when, during a number talk, a student came up with a totally wrong way to get the right answer and it took us several minutes to figure out what the heck had happened.

-I was happy when, rather than lecturing a student who has missed class and done a terrible job on homework, I just started going through examples with the student and found myself enjoying it.

-I was happy when tracking Jill Stein’s fundraising and attempting to guess what function would fit it best.

-This past year, I was happiest when I saw and did for myself the derivation of an explicit formula for the Fibonacci sequence.

Can you spot it? Subtle, huh? I FLIPPING LOVE MATH, and I am happiest when I am discussing and doing interesting math with my students. I am miserable when I’m fighting behavior and grading boring assignments.

There’s a pretty easy fix for this: Don’t give boring assignments and give students math that is interesting and helps to quell the behavior because they want to do the math. That is clearly easier said than done, but it’s pretty easy to motivate me to work for it because I’m clearly so much happier for it.

So if you have mathematically fun and inspiring things, please send them to me. Here are a couple to get you started thinking:

-A complete Venn diagram (all intersections accounted for) can only be rotationally symmetric if the number of sets is prime. WHAT!?!? That’s insane. Here’s an 11 set venn diagram and the shape of one of its sets. (Took the pictures at Macalester College, not sure of the artist-mathematician)

-Apparently ln(1) is complex. Don’t totally get this one yet, but goodness gracious am I totally into figuring it out. (If you get it, don’t ruin it for me.)

We did something mind-blowing in class yesterday (where I am a student, not the teacher). We used the Cantor set to create a continuous, onto function from the interval [0,1] to the unit square!! As in, we have a function that maps points from an interval to a square and covers every single point in the square! I am really excited about this and want to play with it a bunch more!! It’s called a space-filling curve. I should be studying for finals right now, but if you’re interested I can send you some information on them next week… In the meantime, you can find some visualizations on Wikipedia.

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