Surfaces and Solids of Revolution: Using Wolfram|Alpha’s “Virtual Potter’s Wheel”
Before today's 3D printing technology allowed us to make objects of virtually any shape, humanity was limited in the kind and precision of shapes we could produce. Driven to overcome these limitations, we gradually invented a series of machines that could create ever-more-complicated types of shapes, culminating (just before the 3D printer) in machines like this multiaxis computer-numerical-controlled (CNC) mill:
The first of this series of machines was perhaps the potter's wheel, which allowed us to make precisely round objects of any profile. To me, it still seems a bit magical to watch as potters trace out a curve with their hands, and seeing, as the wheel spins, that curve get copied all the way around the vase: