Grassmann algebra is an algebra for Geometry
Continuation Page: 2. On this page we continue a series of graphics from Volume 1 using the entities and operations of the algebra as direct inputs to the drawing routines. Operations include the exterior product for combining entities, and the regressive product for finding their common components. The entities of the algebra can represent vectors, bivectors and multivectors, points, lines, planes, and multiplanes. Projective geometry of n-space is subsumed by the algebra, and many of its theorems reduced to the vanishing of products of the entities. From these entities, higher order objects can be defined: for example curves, surfaces, simplexes or regions of space. Expressions involving these may often be considered as a prescription to construct them. Grassmann algebra is an algebra par excellence for geometry. Animated with systems like Mathematica it also has the potential to become an algebra for dynamic simulations in fields such as physics, engineering and game development.