Build a Brachistochrone and Captivate Your Class

Summary

Introduction

Cliff Long (1931–2002) [5] was a master teacher whose office was a wonderful place to visit, for it was crammed with a wealth of teaching devices. From his early Bug on a Band [6], to his slides and flexible model of quadratic surfaces [3,4], to his head of Abraham Lincoln made with a computer-controlled milling machine [1], and his fascination with knots [7], Cliff was always on the lookout for new ways to illustrate mathematical concepts.

As a young faculty member I went to his office whenever I wondered how best to present some topic in class. He had thought long and hard about everything he taught and was full of ideas about how to enhance learning. Cliff was my mentor and I learned an immense amount about teaching from him.

Of all the things in his office, my favorite was his brachistochrone. I borrowed it to use in talks whenever the Bernoullis were mentioned. The brachistochrone problem was my favorite way to end a class on the integral calculus, for it provided a lovely way to review many of the topics we had studied [10]. Shortly before I retired from Bowling Green State University in 1998, Cliff talked to me about an improved design for the brachistochrone and asked for my suggestions. Little did I know that he was making one for me. I was honored.

Parametric equations

When introducing the topic of parametric equations, a good way to proceed is to arrive in the classroom with your brachistochrone under your arm.