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How Math (and Vaccines) Keep You Safe From the Flu — Quanta Magazine

My latest column for Quanta Magazine breaks down the mathematics of “herd immunity”. By vaccinating a critical percentage of a population against a disease, the potential spread of the disease through the population will proceed at a linear, not exponential, rate. This herd immunity can mean the difference between a handful of illnesses and a catastrophe.

We start by thinking about how rumors spread.

Let’s say you hear a juicy rumor that you just can’t keep to yourself. You hate rumormongers, so you compromise by telling only one person and then keeping your mouth shut. No big deal, right? After all, if the person you tell adopts the same policy and only tells one other person, the gossip won’t spread very far. If one new person hears the rumor each day, after 30 days it will have spread to only 31 people, including you.

So how bad could it be to tell two people? Shockingly bad, it turns out. If each day, each person who heard the rumor yesterday tells two new people, then after 30 days the rumor will have reached more than a quarter of the world’s population (2,147,483,647 people, or 231 − 1, to be exact). How can such a seemingly small change — telling two people instead of one — make such a big difference? The answer lies in rates of change.

A similar mathematical model can be used to understand the spread of disease. And by unpacking the mathematics behind the basic reproduction number of a disease, we can compute the critical cutoff for herd immunity.

Learn more by reading the full article, which comes with a classroom-ready worksheet and is freely available here.

Apple Pies are Delicious

“Cherry pie is delicious!” Nick said, with a big smile. “Apple pies are, too.” He was explaining his memory trick for remembering the formulas for the circumference and area of a circle. A bunch of his classmates nodded along, many who attended the same middle school as Nick. I didn’t quite get it.

Nick diagrammed it out for me.

“Cherry pie is delicious” –>  C \pi d  –>  C = \pi d

“Apples pies are, too” –>  A \pi r 2  –>  A = \pi r^2

Now, I don’t mind a good mnemonic now and then; I still sing the alphabet song, after all. But this struck me as extremely silly. These formulas get used all the time and they are deeply connected to many other important concepts. Relying on a memory trick creates a flimsy foundation for an important body of knowledge. I decided to show Nick just how flimsy.

The next day in class, I approached Nick. “You know, after thinking about it, I agree with you: apple pies are delicious.” He was pleased. But his smile quickly receded. He wrote something out in his notes. “Wait, that’s not right.”

“So apple pies are not delicious?” I asked.

“It’s ‘Cherry pie is delicious‘.” He showed me the formula.

“But apples pies are delicious, right?”

“Yeah, but that’s just not how it works.”

“This is kind of confusing”, I said. “Oh wait. Now I see. Apple pies are delicious too!” I wrote out A \pi r d 2, followed by A = \pi \frac{rd}{2}. “Perfect!”

“What?”

“See here,” I said. I wrote out  A = \pi \frac{rd}{2} = \pi \frac{r2r}{2} = \pi r^2. “You’re method works perfectly!”

Nick started scribbling more in his notebook. Having maximized confusion, I walked away.

Over the next few days I continued my demonstration. “Cherry pies are delicious, too!” I’d say. Or, “Apple pies are really, really delicious!” I might have even said something like “Some apple pies are to die for.”

My demonstration was successful. Maybe too successful. Nick got the area of circle wrong on the next test.

When I handed it back, he acknowledged my point with a combination of irritation and admiration. Nick never got the area of a circle wrong again. And we never had to talk about his Dear Aunt Sally again, either.

[No mathematical understanding was harmed in this story.]

The Problem with Pentagons — Scarsdale High School

I’m excited to be visiting Scarsdale High School, where I’ll be talking about the recent classification of pentagonal tilings of the plane. In my talk, The Problem with Pentagons, I’ll show how a math problem accessible to high school geometry students has a solution that ultimately spans centuries, cultures, and disciplines. The talk is based in part my recent article for Quanta Magazine.

I’m looking forward to meeting students and teachers, visiting some classes, learning more about Scarsdale HS, and talking about tilings!

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01/28/2018 — Happy Permutation Day!

Today we celebrate a Permutation Day! I call days like today permutation days because the digits of the day and the month can be rearranged to form the year.

Celebrate Permutation Day by mixing things up! Try doing things in a different order today. Just remember, for some operations, order definitely matters!

2017 — Year in Review

Although we are well on our way into 2018 (a semiprime year!), I wanted to take a moment to reflect on a busy 2017, one that included our last Pythagorean Triple day for a while.

One of the biggest events for me this year was the launch of my column for Quanta Magazine. In Quantized Academy I write about the fundamental mathematical ideas that underlie Quanta’s stories on cutting edge science and research. This past year I’ve published columns on symmetry and group theory, gerrymandering, and pentagonal tilings, and some of my pieces have also appeared at Wired. It’s been a great experience (and challenge!) so far, and I’m looking forward to seeing where it goes in 2018.

I also continue to contribute to the NYT Learning Network (like this piece on gerrymandering) and have kept up the tradition of writing about the New York State Math Regents exams in 2017, which included one of the worst Geometry tests I’ve ever seen.

I also read a lot of books this past year, in an attempt to find healthier ways to spend my time, and I posted a list of some of the most interesting things I read in 2017. And thanks to a terrific mini-course on data representation with Mona Chalabi, I was inspired to create this Year in Math graphic.

I’ve continued to work to integrate mathematics and computer science in my classroom. This school year I’ve begun piloting a Mathematical Computing course, which is in part based on the work I’ve been doing in Scratch the past few years. I’ve presented about this work at Math for America, the NCTM Annual Meeting, and I’ve been featured by the Scratch Ed community. I plan on continuing to promote new work this year at similar venues.

I had another busy year speaking about mathematics, teaching, and technology. In addition to presenting at conferences like the NCTM Annual Meeting, I delivered the opening keynote at the inaugural MfA Summer Think conference, spoke at a STEM Grand Challenges event hosted by 100kin10, and participated in a panel discussion at the Global Math Week Symposium. I also designed and ran an interactive exhibit at the 2017 World Science Festival. Perhaps my biggest speaking honor this past year was keynoting Math for America’s annual Fall Function, where Giselle George-Gilkes and I spoke to 1,600 teachers and guests about the impact MfA has had on our careers. I already have a lot planned for 2018, but those with speaking inquiries can contact me here.

As always, I’m thankful to be able to reflect on a fulfilling professional year, and I look forward to another good one in 2018.

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