## The Geometry of Surfaces of Revolution |

**Andrew D. Hwang**

College of the Holy Cross

November 13, 2002

4:15 pm

Bailey Hall 201

A classical surface of revolution is an object having an axis of rotational symmetry, such as a sphere, cone, or a piece of furniture turned on a lathe. As Every Calculus Student Knows [tm], a surface of revolution is obtained by revolving the graph of a function about an axis. In this talk, we'll investigate "abstract" surfaces of revolution from the point of view of 2-dimensional beings who live inside such a "universe", with particular attention to the following questions:

- How could such beings prove that their universe is curved without reference to a third dimension?

- In what coordinate system is the curvature of their universe most simply described? (A convincing answer will be given.)

- Do all such universes arise as surfaces of revolution in the calculus sense? If not, can we visualize "exotic" surfaces?
The only prerequisites are geometric imagination and a bit of calculus.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Sat Apr 21 15:30:38 EDT 2018 |