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The Basic Algebra Behind Secret Codes and Space Communication — Quanta Magazine

How can you use systems of linear equations to send secret messages? Just do what NASA does! In my latest column for Quanta Magazine I explore the school math behind Reed-Solomon codes, which are used to safely and securely send data across the solar system.

Space exploration requires tremendous precision. When you’re landing a rover on Mars 70 million miles away from the nearest service station, you need to maximize efficiency and prepare for the unexpected. This applies to everything from spacecraft design to data transmission: Those messages returning to Earth as a steady stream of 0s and 1s are bound to contain some errors, so you need to be able to identify and correct them without wasting precious time and energy.

That’s where math comes in. Mathematicians have invented ingenious ways to transmit and store information. One surprisingly effective method uses Reed-Solomon codes, which are built on the same basic algebra that students learn in school. Let’s drop in on a math class to see how Reed-Solomon codes help transmit and secure information while correcting any costly errors that pop up.

The full article is freely available is here.

By MrHonner, 2 years2 years ago

Resources Teaching Writing

2022 — Year in Review

In keeping up with (what is now a 10-year!) tradition, here’s a brief review of my professional year.

Without question my biggest professional accomplishment of 2022 was the publication of my book, Painless Statistics. People are buying it and even saying nice things about it! From start to finish it was an incredible learning process, and I now know what is meant by the saying “It is better to have written a book than to write one.”

I was happy to resume giving talks and workshop again in person in 2022. In the spring I returned to Queen’s College to speak to soon-to-be math teachers about making math by design. And after two years of remote-only teacher workshops, I was thrilled to return to the Math for America offices for The Geometry of Linear Algebra. It’s been exciting to learn so much linear algebra as I teach it, and I already have new workshops and talks scheduled for 2023.

On top of publishing Painless Statistics, it was another busy year of writing. As usual my column for Quanta Magazine provided a year full of the best kind of mathematical challenges, and I had a blast writing about brownie bake-offs and geometric dissections, different kinds of infinities, and Wordle, among other things. And I reviewed Ben Orlin’s book Math Games with Bad Drawings for the American Mathematical Monthly.

Above all, it was just nice to have a professional year that seemed to be trending toward normal.

For the first time in 5 years my school year planning can begin with "Everything I need to do this year can be done as I did it last year". A welcome change!
— Patrick Honner (@MrHonner) August 5, 2022

Here’s to an even more normal 2023!

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By MrHonner, 2 years2 years ago

Uncategorized Writing

Review — Math Games with Bad Drawings

It was a pleasure to review Ben Orlin’s wonderful book Math Games with Bad Drawings in the American Mathematical Monthly. The review is available online, with subscriber access, here, and will appear in the next print edition of the Monthly.

And in case you’re still shopping, Math Games would make a fabulous holiday gift for the math enthusiastic, math teacher, math student, or math parent in your life!

By MrHonner, 2 years2 years ago

Geometry Writing

The Geometry of Brownie Bake Offs — Quanta Magazine

In my latest column for Quanta Magazine I combine my love of geometric dissections with my appreciation of The Great British Bake Off.

Gina the geometry student stayed up too late last night doing her homework while watching The Great British Bake Off, so when she finally went to bed her sleepy mind was still full of cupcakes and compasses. This led to a most unusual dream.

There’s a remarkable result in geometry that any two polygons of equal area are “scissors congruent”. In my column I explain what this means, why it’s true, and how it connects to some recent research about a famous impossible problem!

You can read the full article here.

By MrHonner, 3 years3 years ago

Numbers Teaching Writing

How Big is Infinity? — Quanta Magazine

My latest column for Quanta Magazine explores one of my favorite topics: infinity!

At the end of the Marvel blockbuster Avengers: Endgame, a pre-recorded hologram of Tony Stark bids farewell to his young daughter by saying, “I love you 3,000.” The touching moment echoes an earlier scene in which the two are engaged in the playful bedtime ritual of quantifying their love for each other. According to Robert Downey Jr., the actor who plays Stark, the line was inspired by similar exchanges with his own children.
The game can be a fun way to explore large numbers:
“I love you 10.”
“But I love you 100.”
“Well, I love you 101!”
This is precisely how “googolplex” became a popular word in my home. But we all know where this argument ultimately leads:
“I love you infinity!” “
Oh yeah? I love you infinity plus 1!”

Learn how a staple of high school math — functions — can help mathematicians understand infinity and even describe the different kinds of infinities there are! The full column is available here and includes a few challenging exercises at the end.

By MrHonner, 3 years3 years ago

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