Geometry

   

Additional Solutions of the Limiting Case "CLP" of the Problem of Apollonius via Vector Rotations using Geometric Algebra

Authors: James A. Smith

This document adds to the collection of solved problems presented in References [1]-[6]. The solutions presented herein are not as efficient as those in [6], but they give additional insight into ways in which GA can be used to solve this problem. After reviewing, briefly, how reflections and rotations can be expressed and manipulated via GA, it solves the CLP limiting case of the Problem of Apollonius in three ways, some of which identify the the solution circles' points of tangency with the given circle, and others of which identify the solution circles' points of tangency with the given line. For comparison, the solutions that were developed in [1] are presented in an Appendix.

Comments: 38 Pages.

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Submission history

[v1] 2016-08-24 18:28:40
[v2] 2016-08-27 23:19:26

Unique-IP document downloads: 34 times

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