Sphere-Cylinder Intersection (Paperback)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the theory of analytic geometry for real three-dimensional space, the intersection between a sphere and a cylinder can be a circle, a point, the empty set, or a special type of curve. For the analysis of this situation, assume (without loss of generality) that the axis of the cylinder coincides with the z-axis; points on the cylinder (with radius r) satisfy x2 + y2 = r2. We also assume that the sphere, with radius R is centered at a point on the positive x-axis, at point (a,0,0). Its points satisfy (x a)2 + y2 + z2 = R2. The intersection is the collection of points satisfying both equations.