Book contents
- Frontmatter
- Preface
- Introduction
- Contents
- Learning from the Medieval Master Masons: A Geometric Journey through the Labyrinth
- Dem Bones Ain't Dead: Napier's Bones in the Classroom
- The Towers of Hanoi
- Rectangular Protractors and the Mathematics Classroom
- Was Pythagoras Chinese?
- Geometric String Models of Descriptive Geometry
- The French Curve
- Area Without Integration: Make Your Own Planimeter
- Historical Mechanisms for Drawing Curves
- Learning from the Roman Land Surveyors: A Mathematical Field Exercise
- Equating the Sun: Geometry, Models, and Practical Computing in Greek Astronomy
- Sundials: An Introduction to Their History, Design, and Construction
- Why is a Square Square and a Cube Cubical?
- The Cycloid Pendulum Clock of Christiaan Huygens
- Build a Brachistochrone and Captivate Your Class
- Exhibiting Mathematical Objects: Making Sense of your Department's Material Culture
- About the Authors
Build a Brachistochrone and Captivate Your Class
- Frontmatter
- Preface
- Introduction
- Contents
- Learning from the Medieval Master Masons: A Geometric Journey through the Labyrinth
- Dem Bones Ain't Dead: Napier's Bones in the Classroom
- The Towers of Hanoi
- Rectangular Protractors and the Mathematics Classroom
- Was Pythagoras Chinese?
- Geometric String Models of Descriptive Geometry
- The French Curve
- Area Without Integration: Make Your Own Planimeter
- Historical Mechanisms for Drawing Curves
- Learning from the Roman Land Surveyors: A Mathematical Field Exercise
- Equating the Sun: Geometry, Models, and Practical Computing in Greek Astronomy
- Sundials: An Introduction to Their History, Design, and Construction
- Why is a Square Square and a Cube Cubical?
- The Cycloid Pendulum Clock of Christiaan Huygens
- Build a Brachistochrone and Captivate Your Class
- Exhibiting Mathematical Objects: Making Sense of your Department's Material Culture
- About the Authors
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.
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- Hands on HistoryA Resource for Teaching Mathematics, pp. 153 - 162Publisher: Mathematical Association of AmericaPrint publication year: 2007