Arch Mathematics (UMAP)

In the springs of 1999 and 2001, I incorporated a series of Mathematica projects or "labs" into a vector analysis course. These labs used the technology of a computer algebra system to develop further a particular concept, solve an application, or bring together several disjoint ideas. By far the most popular lab was the one that explored the mathematics behind the Jefferson National Expansion Memorial, commonly called the St. Louis Arch, or just the Arch. In the lab, students found a parametrization of the Arch and used this parametrization to compute its surface area. Alternative approaches to this problem include Thayer [1982], Edwards and Penney [1994a, 477-478; 1994b], and Banks [1998, 161-166].

Table of Contents:

INTRODUCTION

PREREQUISITES

THE ARCH

GEOMETRY OF THE ARCH

PARAMETERIZATION

SURFACE AREA

CONCLUSION

ANSWERS TO THE EXERCISES

REFERENCES

ABOUT THE AUTHOR