Author

Todd Huckaby

Date of Award

2013

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Mullins, David

Keywords

Curved Axis Revolutions, Differential Geometry, Volumes of Rotation

Area of Concentration

Mathematics

Abstract

Motivated by standard solids of revolution computable by elementary calculus methods this thesis develops a construction of solids of revolution with a curved axis. We show that the volumes obtained do not depend on the curvature of the axis. In H3, we show by construction there is no straight-forward generalization. A partial generalization is conjectured to exist for curves in a horizontal plane because the natural map between the horizontal cylinder to the horizontal torus is seen to preserve volume in an example.

Share

COinS