Why Triangles are Easy and Tetrahedra are Hard — Quanta Magazine

My latest column for Quanta Magazine is a celebration of the Triangle Angle Sum theorem, a favorite result from high school geometry.

Do you think there’s a triangle whose angles measure 41, 76 and 63 degrees?

At first, answering this may seem easy. From geometry class we know that the sum of the measures of the interior angles of a triangle is 180 degrees, and since 41 + 76 + 63 = 180, the answer must be yes.

But there’s more to this question than meets the eye.

From triangles we move to tetrahedra, where a surprisingly simple question about angles wasn’t resolved until 2020. You can read all about it here.

2021 in Tweets

Here’s a tweet-per-month review of my 2021. Enjoy!

January

February

March

April

May

June

July

August

September

October

November

December

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2021 — Year in Review

A return to in-person schooling was the biggest news of 2021. I don’t want to be accused of burying the lede.

It’s been great to be back. It’s also been an interesting challenge trying to weave together what I learned over the past year-and-a-half as a full-time remote teacher with what I was doing in-person before that. Add in new colleagues, redefined priorities for teacher teams, and a brand new course to teach and it’s been a pleasantly busy return to the building.

I’ve also stayed busy with a variety of talks and webinars this past year. As always I ran several workshops for Math for America, like Bringing Modern Math into the Classroom in January and It’s All Linear Algebra in November. This summer I participated in a roundtable discussion at the National Museum of Mathematics on math education. And I was thrilled and honored to run a week of morning math for the Park City Math Institute’s Teacher Leadership Program, satisfying two long-standing professional goals: to participate in PCMI and to finally make sense of complex multiplication!

I continued to write my column for Quanta Magazine, which is on ongoing professional highlight. The year started with the crooked geometry of round trips (an article that was picked up by Wired magazine) and covered everything from hot dogs to goats to tricky job interview questions.

I was proud to keep up my Remote Learning Journal throughout the 2020-21 school year, and was happy to have the opportunity to reflect on the totality of my experience on the MAA’s Math Values blog, where I published “Let’s Remember the Year Everyone Wants to Forget“. I was also able to capture some fun moments in writing this past year, with a short story about an absolutely brilliant student solution to a calculus problem as well as a Seussian poem proof of the irrationality of the square root of 2.

Without question my single biggest professional project this year, writing or otherwise, was getting a manuscript submitted. I knew it would be more work than I expected, and it was. But the process was exciting and eye-opening and worthwhile, and I am thrilled that Barron’s Painless Statistics will be out in June 2022.

It’s been another year full of challenges, changes, and opportunities, and I hope 2022 brings us a healthier balance of all those things.

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What Hot Dogs Can Teach Us About Number Theory — Quanta Magazine

My latest column for Quanta Magazine was inspired by the true story of me being frustrated by a six-pack of hot dogs.

If you’ve ever had to buy hot dogs for a cookout, you might have found yourself solving a math problem involving least common multiples. Setting aside the age-old question of why hot dogs usually come in packs of 10 while buns come in packs of eight (you can read what the National Hot Dog and Sausage Council has to say about it here), let’s stick to the math that gets our hot dogs to match our buns. A simple solution is to buy eight packs of hot dogs and 10 packs of buns, but who needs 80 hot dogs? Can you buy fewer packs and still make the numbers match?

Trying to get hot dogs and buns to match up is a simple exercise in least common multiples, but it also opens to the door to more complicated math using the Chinese Remainder Theorem, a 2,000 year old algorithm for solving systems of congruences. Learn more by reading the article, which is freely available here.

Workshop — It’s All Linear Algebra

Tonight I’ll be running my workshop “It’s All Linear Algebra” for teachers at Math for America.

This workshop is designed to show teachers how the big ideas of linear algebra — linear combinations, vectors, systems, dependence — are present in all the courses in the middle school and high school curriculum. Making these connections can help enrich the teaching of these topics in earlier courses, create threads that connect ideas throughout the sequence, and preview what lies ahead in more advanced courses.

This workshop is based on my experience teaching linear algebra in high schools for the past 10 years. After a short break I’m teaching it again this year, and I’m having a blast revisiting the ideas with a fresh perspective.

I’ve been learning a lot this year and I’m excited to share my experiences, and some great math, with teachers in this workshop.

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