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.
Recommended Citation
Huckaby, Todd, "CURVED AXIS REVOLUTIONS" (2013). Theses & ETDs. 4801.
https://digitalcommons.ncf.edu/theses_etds/4801