Surfaces Associated with Curves

Introduction

This lab acts as a transition between the theory of curves and the theory of surfaces. In contrast to a curve, which depends on a single parameter, a surface must depend on two parameters. We can learn more about curves by using them as foundations for building certain types of surfaces, and begin learning about surfaces as well in the process. Examples of surfaces that are naturally associated with curves are cones, cylinders, strips, and tubes. In this laboratory, we will explore basic phenomena associated with these surfaces, and begin our study of properties such as area.