Conformal Mappings in Geometric Algebra

Abstract

In 1878 William Kingdon Clifford wrote down the rules for his geometric algebra, also known as Clifford algebra. We argue in this paper that in doing so he laid down the groundwork that is profoundly altering the language used by the mathematical community to express geometrical ideas. In the real estate business everyone knows that what is most important is location. We demonstrate here that in the business of mathematics what is most important to the clear and concise expression of geometrical ideas is notation. In the words of Bertrand Russell, …A good notation has a subtlety and suggestiveness which at times make it seem almost like a live teacher. Heinrich Hertz expressed much the same thought when he said, One cannot escape the feeling that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than we originally put into them.