Writing

How to Solve Equations That Are Stubborn as a Goat — Quanta Magazine

My latest column for Quanta Magazine is about the infamous grazing goat. Perhaps you’ve met one.

If you’ve ever taken a math test, you’ve probably met a grazing goat. Usually it’s tied to a fence post or the side of some barn, left there by an absent-minded farmer to graze on whatever grass it can reach. When you meet a grazing goat, your job is to calculate the total area of the region it can graze on. It’s a math test, after all.

Math problems involving grazing goats have been around for over a hundred years, but it wasn’t until last year that one particularly stubborn goat problem was solved exactly. Read my column for some examples of grazing goat problems you might find on a geometry test, and about the problem that took mathematicians over a century to finally solve.

By MrHonner, ago

The Mysterious Math of Perfection — Quanta Magazine

My latest column for Quanta Magazine explores the mathematics of perfect numbers. Humans have been studying perfect numbers for thousands of years, but we still don’t know if an odd perfect number exists!

Euclid laid out the basics of perfect numbers over 2,000 years ago, and he knew that the first four perfect numbers were 6, 28, 496 and 8,128. Since then, many more perfect numbers have been discovered. But, curiously, they’re all even. No one has been able to find an odd perfect number, and after thousands of years of unsuccessful searching, it might be tempting to conclude that odd perfect numbers don’t exist. But mathematicians haven’t been able to prove that either. How is it that we can know so much about even perfect numbers without being able to answer the simplest question about an odd one? 

With some basic number theory and an assist from a famous formula from Algebra class, we can get pretty far into the world of perfect numbers. So read the full article here, and be sure to stick around for the exercises at the end!

By MrHonner, ago

The Crooked Geometry of Round Trips — Quanta Magazine

My latest column for Quanta Magazine explores what round-the-world trips would look like if we didn’t live on a sphere.

Have you ever wondered what life would be like if Earth weren’t shaped like a sphere? We take for granted the smooth ride through the solar system and the seamless sunsets afforded by the planet’s rotational symmetry. A round Earth also makes it easy to figure out the fastest way to get from point A to point B: Just travel along the circle that goes through those two points and cuts the sphere in half. We use these shortest paths, called geodesics, to plan airplane routes and satellite orbits.

But what if we lived on a cube instead? Our world would wobble more, our horizons would be crooked, and our shortest paths would be harder to find.

Classification of geodesic paths on platonic solids didn’t happen until relatively recently, and the case of the dodecahedron offers quite a surprise! To learn more, read the full article here.

By MrHonner, ago

The Best Writing on Mathematics 2020

A piece I wrote last year was selected for The Best Writing on Mathematics 2020, published by Princeton University Press. It’s an incredible and quite unexpected honor.

I have known about this for several months, but I was still a bit shocked to see this:

I’ve been writing about math and teaching for years, but I never dreamed of being included in a collection of “The Best Writing on Mathematics” alongside writers like Steven Strogatz, Erica Klarreich, and John Carlos Baez.

I’m grateful to the editor, Mircea Pitici, for selecting “On Your Mark, Get Set, Multiply” for the collection, and to everyone at Quanta Magazine, where the piece was originally published. I am very fortunate to write for Quanta, where I have incredible writers to learn from and an editor, Quanta’s founder and Editor-in-Chief Thomas Lin, who has invested a great deal of time and effort into helping me become a better writer.

You can learn more about Princeton University Press’s The Best Writing on Mathematics 2020 here.

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By MrHonner, ago

Some Math Problems Seem Impossible. That Can Be a Good Thing — Quanta Magazine

In my latest column for Quanta Magazine I write about the secret power of impossible math problems.

Construct a convex octagon with four right angles.

It probably says a lot about me as a teacher that I assign problems like this. I watch as students try to arrange the right angles consecutively. When that doesn’t work, some try alternating the right angles. Failing again, they insert them randomly into the polygon. They scribble, erase and argue. The sound of productive struggle is music to a teacher’s ears.

Working on impossible problems has a way of helping us better understand what is possible in math, and the impossible plays an important role in the history of mathematics. In my column I explain using several examples, and include a few extra exercises to play around with. The impossible can be frustrating, but also fun!

The entire article is freely available here.

By MrHonner, ago
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