An Introduction to Inversion in an Ellipse
Jos\'e L. Ram\'irez
TL;DR
This paper explores the mathematical properties of inversion in ellipses, extending classical circle inversion concepts to ellipses and related curves, and generalizes the Pappus Chain theorem in this context.
Contribution
It introduces a comprehensive study of ellipse inversion, including properties, transformations of various curves, and a generalization of the Pappus Chain theorem.
Findings
Inversion in an ellipse generalizes circle inversion.
Properties of inversion for lines, ellipses, and other curves are characterized.
The Pappus Chain theorem is extended to ellipses.
Abstract
In this paper we study the inversion in an ellipse and some properties, which generalizes the classical inversion with respect to a circle. We also study the inversion in an ellipse of lines, ellipses and other curves. Finally, we generalize the Pappus Chain with respect to ellipses and the Pappus Chain Theorem.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Advanced Numerical Methods in Computational Mathematics · Soil, Finite Element Methods