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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, 4 years3 years ago

Resources Teaching

PCMI 2021

I’m excited to be a part of the Park City Math Institute’s 2021 upcoming summer program!

PCMI provides immersive mathematical experiences for scientists, students, and educators through their summer programs. This year, I’ll be running a week-long session for PCMI’s Teacher Leadership Program titled Complex Geometry Made Simple. Here’s the course description:

The complex numbers are one of the great achievements of algebra, but their geometry may be even more compelling. Join us as we explore the complex connections between elementary geometry, inversion, rotations, functions, and more! The shortest path to real truth may involve a detour through the complex plane, but in this course we’ll be sure to take time to enjoy the journey.

PCMI’s Teacher Leadership program runs July 12 — 30 and includes courses on Fibonacci Recurrences, led by Daryl Yong and Bowen Kerins, and Hands on Combinatorics, led by Brian Hopkins. You can find out more information on the programs, including how to apply, here.

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By MrHonner, 4 years4 years ago

Numbers Resources Writing

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, 4 years3 years ago

Resources Teaching

Workshop — Bringing Modern Math into the Classroom

This Thursday I’ll be running my workshop “Bringing Modern Math into the Classroom” for teachers at Math for America.

In this webinar participants will engage with mathematics at the edge of our understanding. We’ll look at examples of math that’s being invented and discovered right now, and see how it connects to what is happening in classrooms.

We’ll play games, explore patterns, and make conjectures in arithmetic, algebra, and geometry. The goal is for participants to leave not only with a better understanding of how school math and research math are connected, but how to better communicate that connection to students.

This workshop is based on the work I’ve done in my Quantized Academy column for Quanta Magazine. I’ve run similar workshops in past years, and I recently gave a talk on this topic at the NCTM 2020 Virtual Conference. But this week’s workshop is all new, and I’m looking forward to bringing some new ideas and new math to play around with!

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By MrHonner, 4 years4 years ago

Geometry Resources Writing

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, 4 years3 years ago

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