## A Mathematician Solves a Maze

A couple weeks ago, I was at a Cub Scout event with my son. Each of us had a placemat with, among other things, a maze on it. I approached the maze like I, as a mathematician, approach most problems:… Continue Reading

## A Mathematician Ties a Tie

I learned to tie a tie before I became a mathematician. I was still just a kid when I learned. My grandparents taught me to make a basic Windsor knot. I could get that part right, but the length would invariably be… Continue Reading

## Self-Diagram

A few weeks ago, I stumbled across this gem of a geometry problem from an old MATHCOUNTS exam: The intersection of a circular region of radius $3$ inches and a circular region of radius $2$ inches has area $\pi$ square… Continue Reading

## Happy Approximation to Pi Day!

March 14 is one of my least favorite days of the year. While most math teachers revel in Pi Day, I spend my 3/14s frustrated that we waste an opportunity to pay homage to one of the most important numbers in… Continue Reading

## Square Sum Puzzles

A couple nights ago, my son was finishing up his nightly Beast Academy and enjoying the puzzles so much that he took his workbook with him at bedtime and continued to work for another hour! He was in a section of… Continue Reading

## Bagel Math

The Three Utility Problem is a classical mathematical puzzle: Three customers, Alice, Bob, and Charlie, all want to connect their houses to three different utilities, Electricity, Gas, and Water. Can each customer run a line to each utility company in… Continue Reading

## My Little Monster

My oldest son has good taste. For as long as he’s been in school, his favorite subject has been math. I was not his first math teacher. That honor goes to video games. He learned to count by tracking the… Continue Reading

## Hyperbolic Space

In Spring of 2016, I taught a new elective at IMSA called Modern Geometries. The course started with a deep dive into Euclid’s Elements followed by a careful analysis of the consequences when some of Euclid’s (often unstated) premises were challenged.… Continue Reading

## A Question on Ellipses, Part 3

In the last two posts, we’ve looked at the question What is the set of points of intersection of a normal line of an ellipse with its major axis, barring the normal lines at the endpoints of the major axis?… Continue Reading

## A Question on Ellipses, Part 2

In the last post, I posed the question: What is the set of points of intersection of a normal line of an ellipse with its major axis, barring the normal lines at the endpoints of the major axis? The most… Continue Reading