The Algebra of Geometry
Greg Wilmot
Pascal's triangle is known to relate to both simplices and Clifford algebra with the later providing a complete representation. This relationship allows each Clifford algebra to be derived from the associated simplex which exposes the connection to geometry justifying the terminology geometric algebra. Simplices are also related to Pfaffians and this close connection can be used to explain the Pfaffian structure of the algebra. An example is the grad operator acting on a product of two vectors to bring all three primary vector calculus identities into one equation with geometric identification of each component.