The Simple Math Problem We Still Can’t Solve — Quanta Magazine

My latest column for Quanta Magazine explores a simple math problem that no one should try to solve. Even though everyone has probably tried to!

This column comes with a warning: Do not try to solve this math problem.

You will be tempted. This problem is simply stated, easily understood, and all too inviting. Just pick a number, any number: If the number is even, cut it in half; if it’s odd, triple it and add 1. Take that new number and repeat the process, again and again. If you keep this up, you’ll eventually get stuck in a loop. At least, that’s what we think will happen.

The infamous Collatz conjecture has been capturing the attention of mathematicians and recreational problem solvers since it was first introduced in 1937. It seems so simple, yet no one has been able to prove it. Recent progress has been made, however, by none other than Terry Tao, one of the world’s great mathematicians.

You can learn more about Collatz conjecture in my column. Just don’t try to solve it! You’ve been warned.

MfA Workshop – A Crash Course in Geogebra

Today I’ll be facilitating “A Crash Course in Geogebra” as part of Math for America‘s summer professional development series.

In response to the challenges and uncertainty of the upcoming school year, MfA teachers have been sharing ideas and expertise with the community this summer. My experiences using Geogebra during NYC’s emergency remote learning led me to develop this workshop.

Geogebra is an invaluable tool for doing mathematics under normal circumstances, but its versatility as a mathematics environment, a demonstration tool, and an assessment platform is even more important in this era of remote and hybrid learning. In addition to reviewing the basics of Geogebra in the webinar, I’ll also share specific classroom strategies and student project ideas for implementation in either face-to-face or remote/hybrid learning.

As I said recently, I can’t imagine teaching geometry remotely without Geogebra. And while I can imagine teaching geometry face-to-face without it, I wouldn’t want to!

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Coding Math at a Distance — #NCTM100

I’m excited to be co-presenting “Coding Math at a Distance” this week as part of NCTM’s 100 Days of Professional Learning webinar series.

I’ll be working with Mike Larson and Ashley Goetz, the teachers who co-founded CSandMath.org, and our webinar focuses on simple ways teachers can use computer science to enrich math learning. Mike, Ashley, and I have all been involved in this work for many years, and we’re excited to share both big ideas and classroom-ready resources for teachers.

We’ll pay particular attention to the ways in which integrating CS and math makes sense for remote and hybrid learning environments. We know teachers are looking for new approaches to engagement, assessment, and collaboration in this era of remote learning, and integrated math and CS projects offer lots of exciting opportunities, for both teachers and students.

The webinar is free and part of NCTM’s centennial celebration. You can find out more, and register, here. You can also access resources from our session: Our takeaway document; a Scratch studio that includes code examples; and a set of function-based extension projects.

UPDATE: The full webinar has been posted on the NCTM website.

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AMS Math in the Media — Interview

I was recently interviewed for the American Mathematical Society’s Math in the Media column, in which I answer some questions my Quanta Magazine column and about writing about math for the public. I was asked specifically about my column on the universal covering problem.

Why did you recently choose to write about the universal covering problem?
It’s such a fun mathematical story to tell, with meaningful connections to high school geometry. And there’s something uniquely mathematical about studying a shape for a hundred years and still not knowing exactly what it looks like. I enjoy bringing those experiences to others.

The rest of the short interview can be found here.

The Math of Social Distancing is a Lesson in Geometry — Quanta Magazine

My latest column for Quanta Magazine connects the geometry of social distancing, a topic on everyone’s mind right now, with sphere packing, a problem mathematicians have been working on for hundreds of years.

Determining how to safely reopen buildings and public spaces under social distancing is in part an exercise in geometry: If each person must keep six feet away from everyone else, then figuring out how many people can sit in a classroom or a dining room is a question about packing non-overlapping circles into floor plans.

In two dimensions, the sphere packing problem is really the circle packing problem, and the best way to pack circles in the plane is known. But it was only recently that mathematicians settled the question about how to most efficiently pack spheres in dimensions 8 and 24. And there are still many open questions in other dimensions!

You can read the entire article here.

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