Date of Award
8-1970
Document Type
Thesis
Degree Name
Master of Science
Degree Discipline
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 University
This 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