DISCRETIZATION OF REGULAR SURFACES PRESERVING CURVATURE

Author

Connor Welch

Date of Award

2021

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

McDonald, Patrick

Area of Concentration

Mathematics

Abstract

We provide a treatment of the material required to prove the Gauss-Bonnet Theorem. Having developed the classical material, we discuss approximation of surfaces via triangularization and introduce a discrete version of Gauss curvature for piecewise linear spaces. Using our definition of discrete Gauss curvature, we prove a version of the Gauss-Bonnet Theorem for piecewise linear space.

Recommended Citation

Welch, Connor, "DISCRETIZATION OF REGULAR SURFACES PRESERVING CURVATURE" (2021). Theses & ETDs. 6164.
https://digitalcommons.ncf.edu/theses_etds/6164