Authors: James A. Smith
This document adds to the collection of solved problems presented in References -. The solutions presented herein are not as efficient as those in , 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  are presented in an Appendix.
Comments: 38 Pages.
Unique-IP document downloads: 54 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.