Universal Geometric Algebra
Since Grassmann’s original work “Ausdehnungslehre” in 1844, and William Kingdom Clifford’s later discovery of “geometric algebra” in 1878, the mathematical community has been puzzled by exactly how these works fit into the main stream of mathematics. Certainly the importance of these works in the mathematics at the end of the 20th Century has been recognized, but there has been no general agreement about where and how the methods should be utilized. In this chapter, I wish to show how the works of Grassmann and Clifford can be integrated into the mainstream of mathematics in such a way as to require as little as possible changes to the main body of mathematics as we know it today. As has been often repeated by Hestenes and others, geometric algebra should be seen as a great unifier of the geometric ideas of mathematics.
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