Resources

Math that Moves the Needle — Quanta Magazine

My latest column for Quanta Magazine explores a century-old geometry problem that anyone who’s ever performed a three-point turn can appreciate.

Imagine you’re rolling down the street in a driverless car when you see a problem ahead. An Amazon delivery driver got their van halfway past a double-parked UPS truck before realizing they couldn’t make it through. Now they’re stuck. And so are you.

There’s a fun math problem here about how much space you need to turn your car around, and mathematicians have been working on an idealized version of it for over 100 years. It started in 1917 when the Japanese mathematician Sōichi Kakeya posed a problem that sounds a little like our traffic jam. Suppose you’ve got an infinitely thin needle of length 1. What’s the area of the smallest region in which you can turn the needle 180 degrees and return it to its original position? This is known as Kakeya’s needle problem, and mathematicians are still studying variations of it. Let’s take a look at the simple geometry that makes Kakeya’s needle problem so interesting and surprising.

You can read all about the surprising resolution of Kakeya’s needle problem in my full column for Quanta Magazine.

By MrHonner, ago

Jaipur Literature Festival New York

I’m thrilled to be a part of the upcoming Jaipur Literature Festival in New York City, where I’ll be in conversation with mathematician and novelist Manil Suri. Manil’s latest book, The Big Bang of Numbers, is a tour of mathematics from the ground up, allowing the reader to the experience of the power of mathematical creation as Manil constructs the universe using only math. It is a fun, friendly, and one-of-a-kind book.

In our JLF session A Universe Built on Math, Manil and I will be talking about math, writing, teaching, and everything in between. The talk is happening on September 13th at 4:30 pm at the Asia Society. All the details can be found here.

By MrHonner, ago

Math Patterns That Go On Forever but Never Repeat — Quanta Magazine

I wrote a column for Quanta Magazine on the recently discovered “hat tile”, the first ever aperiodic monotile!

Have you ever admired how the slats of a hardwood floor fit together so cleanly, or how the hexagons underneath your bathroom rug perfectly meet up? These are examples of geometric tilings, arrangements of shapes that fit snugly together while filling up space. Two-dimensional tilings are admired all around the world, both for their beauty — as seen in the artistry of mosaics in cathedrals and mosques around the world — and for their utility, in walls and floors everywhere.

In math, tilings are often appreciated for their regular patterns. But mathematicians also find beauty in irregularity. It’s this kind of beauty that a retired print technician was seeking when he recently discovered the first “aperiodic monotile”— a single tile that fills up the plane in a non-repeating pattern. To get a handle on this big discovery, let’s start by thinking about a simpler problem: how to tile a line.

You can read the full article for free here.

By MrHonner, ago

Math That Lets You Think Locally but Act Globally — Quanta Magazine

My latest column for Quanta Magazine explores some recent results in graph theory that use local information to draw global conclusions, a powerful tool in math! It begins with a puzzle.

In math, as in life, small choices can have big consequences. This is especially true in graph theory, a field that studies networks of objects and the connections between them. Here’s a little puzzle to help you see why.

Given six dots, your goal is to connect them to each other with line segments so that there’s always a path between any pair of dots, with no path exceeding two line segments in length.

You can see the solution to the puzzle and learn how it connects to new results in graph theory by reading the full article here for free.

By MrHonner, ago

The Symmetry That Makes Solving Math Equations Easy — Quanta Magazine

My latest column for Quanta Magazine is about one of the most dreaded mathematical objects in high school math: the quadratic formula!

x=\frac{-b \pm \sqrt{b^2-4ac}} {2a}

As complicated as the quadratic formula is, the cubic formula is much worse, but a simple geometric idea connects the two.

As intimidating as this looks, hiding inside is a simple secret that makes solving every quadratic equation easy: symmetry. Let’s look at how symmetry makes the quadratic formula work and how a lack of symmetry makes solving cubic equations much, much harder. So much harder, in fact, that a few mathematicians in the 1500s spent their lives embroiled in bitter public feuds competing to do for cubics what was so easily done for quadratics.

You can read the full article here.

By MrHonner, ago
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