# Soccer Challenges: Angling for a Shot on Goal

With the World Cup in our hemisphere, and the US squad having started out with a win over Ghana, my thoughts turned to the mathematics of soccer. My friend Henri Picciotto has a nice page about the shooting angle, the angle within which a shot is on goal, so I thought of using … Continue Reading ››

# Drawing Ellipses with a Congruent Triangle Construction

Welcome back to my ongoing series in which I feature interactive Web Sketchpad models that draw conic sections. Today’s installment, like the previous one, focuses on ellipses, and dates back to the 17th-century Dutch mathematician, Frans van Schooten. Below is an image from van … Continue Reading ››

# Arthur Ganson and the Excitement of Construction

I first encountered the kinetic sculptures of Arthur Ganson nearly 20 years ago at the MIT Museum. Ganson is an engineer, artist, and inventor whose machines, when set in motion, display a grace you would not expect from metal, gears, and other industrial objects. Below is a video of one of my favorite … Continue Reading ››

# Wait for a Date

Last year, I wrote a blog post about the following probability question: Two friends arrange for a lunch date between 12:00 and 1:00. A week later, however, neither of them remembers the exact meeting time. As a result, each person arrives at a random time between 12:00 and 1:00 … Continue Reading ››

# The Dog Leash Investigation

Today's guest post is from Marta Venturini, a PhD student in Mathematics Education at Simon Fraser University under a "Cotutelle Agreement" with the University of Bologna, where she's a PhD student in Mathematics. While looking for some tasks that would be suitable for Sketchpad,  I found the “dog leash” problem in a March 2007 Continue Reading ››

# The Wavy Wavy Bridge

At the 2013 Baltimore Regional NCTM Meeting, I gave a presentation on Picturing Functions and Functions of Pictures. In the description of my presentation I’d promised to show how to use Sketchpad to create special effects, so when it came time to prepare, I figured I needed to deliver on my promise. So I wrote a … Continue Reading ››

# Leveraging Sketchpad to Gain Insight Into an Algebra Problem

Several weeks ago, my friend Sandra came to me with a problem posed by one of her algebra students: Find all points that are twice as far from a given point A as they are from a given point B. Sandra and I chose particular locations for points A and B, and got to work solving the … Continue Reading ››

# What Does Rowing Have to Do with Teaching Mathematics?

Harry Parker died this summer, two weeks after coaching the Harvard rowing team to yet another sweep of all four races (varsity, JV, freshmen, and spares) against Yale and two days after accompanying his 1980 … Continue Reading ››

# Taking Ownership of Mathematical Ideas

Of the many reasons that I chose to major in mathematics, perhaps the most compelling to me was this: Mathematics is beautiful. Yes, mathematics could be practical, but it was the sheer beauty of its proofs that left me awestruck. How could I not be impressed, for example, by the elegance and ingenuity of the proof … Continue Reading ››