Calculus B

During the course of Calculus B at Kenyon, one assignment which students ofen have a lot of fun pursing is the "goblets" project. This consists of creating a piecewise-defined function and rotating it about the x axis. This creates a simple solid of revolution which, when rotated 90 degrees counterclockwise about the Z-axis (i.e., when it is "stood upright"), looks like a goblet. This is similar to a lathe in 3-dimensional modeling terminology.

To the right is a three-dimensionally rendered image of one of the goblets from the 1998-99 class, created by Atul Varma. The actual input of the function and creation of the surface of revolution was performed using Waterloo Maple V release 5. You can view a graph of the goblet's generating curve here.

More specifically, the students' goblets had to conform to the following specifications:

• It must be a solid of revolution. (Circularly symmetric.)
• It must hold at least 150 cu. cm. of liquid
• It cannot take any more that 150 cu. cm. of glass to manufacture.
• The ratio of the height of the center of mass to the radius of the base must be no more than 3:1.
• The radius of its stem must be at least 1/4 cm. at its thinnest point.