#### Date of Award

8-1970

#### Document Type

Thesis

#### Degree Name

Master of Science

#### Department

Master of Mathematics

#### Abstract

It is the purpose of this paper to show that the inversion transformation is a useful transformation for simplifying plane figures. The paper is an outgrowth of proving Ptolemy's Theorem (In a cyclic convex quadrilateral the product of the diagonals is equal to the sum of the product of the two pairs of opposite sides). This theorem can be used to prove a fundamental trigonometric identity; namely, sin( A - B ) = sin A cos B - cos A sin B, which will be proved later in the paper.

The writer found an interesting and concise proof of Ptolemy's theorem in Geometry, Volume I by H. Eves, which led him to become interested in the inversion transformation of which Ptolemy's Theorem is one such application.

The writer will now prove Ptolemy's theorem without using inversion. Later in the paper the writer will prove Ptolemy's theorem using inversion.

#### Committee Chair/Advisor

Frederick Gray

#### Publisher

Prairie View A&M College

#### Rights

© 2021 Prairie View A & M UniversityThis work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

#### Date of Digitization

3-22-2022

#### Contributing Institution

John B Coleman Library

#### City of Publication

Prairie View

#### MIME Type

Application/PDF

#### Recommended Citation

Simmons, A. (1970). The Inversion Transformation and Some of Its Applications. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/1380