Examples of Surfaces

In this chapter we will study three very important and commonly occurring classes of surfaces (algebraic surfaces, surfaces of revolution, and ruled surfaces) and envelopes of surfaces. In Section 8.1 we will study surfaces of revolutions and plot the Möbius band and a map on a torus that cannot be colored with six colors. In Section 8.2 we will develop an M-file (the resultant) to deduce the polynomial equations of surfaces. In Section 8.3 we will study ruled surfaces of various types and calculate their striction curves and the distribution parameter. In Section 8.4, using the notion of a tangent plane (see Section 7.2), we will plot some envelopes of families of surfaces (see also Section 6.1 for curves).