|Geometric Algebra: A Foundation of Elementary Geometry with possible Applications in Computer Algebra based Dynamic Geometry Systems
|Dietmar HILDENBRAND and Reinhard OLDENBURG
Geometric Algebra is a very general mathematical system providing simultaneously a geometrification of algebra, and also an algebrification of geometry. As an example, we present a specific Geometric Algebra, that we call Compass Ruler Algebra, which is very well suited to compute similar to working with compass and ruler. Geometric objects such as circles and lines as well as geometric operations with them can be handled very easily inside of the algebra. Gaalop is an easy to handle tool in order to compute and visualize with Compass Ruler Algebra. While a computer algebra system is responsible for the symbolic computations, its visualizing component offers basic DGS (Dynamic Geometry System) functionality.