Date of Award
Master of Science
Master of Mathematics
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.
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Date of Digitization
John B Coleman Library
City of Publication
Simmons, A. (1970). The Inversion Transformation and Some of Its Applications. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/1380