Rotations of Vectors Via Geometric Algebra: Explanation, and Usage in Solving Classic Geometric "Construction" Problems (Version of 11 February 2016)

Authors: James A. Smith

Written as somewhat of a "Schaums Outline" on the subject, which is especially useful in robotics and mechatronics. Geometric Algebra (GA) was invented in the 1800s, but was largely ignored until it was revived and expanded beginning in the 1960s. It promises to become a "universal mathematical language" for many scientific and mathematical disciplines. This document begins with a review of the geometry of angles and circles, then treats rotations in plane geometry before showing how to formulate problems in GA terms, then solve the resulting equations. The six problems treated in the document, most of which are solved in more than one way, include the special cases that Viete used to solve the general Problem of Apollonius.

Comments: 76 Pages.

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Submission history

[v1] 2016-05-22 20:17:30

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