17 OPERATIONAL MODELS FOR GEOMETRIES
Now that we have the conformal model of Euclidean geometry and have seen its effectiveness, it is useful to take a step back and look in a more abstract manner at what we have actually done and why it works so well. That will provide a tentative glimpse of future developments in this way of encoding geometries.
17.1 ALGEBRAS FOR GEOMETRIES
A geometry (affine, Euclidean, conformal, projective, or any kind) is characterized by certain operators that act on the objects of the geometry. These objects can range from geometrical entities such as a triangle to properties such as length, so they may have various dimensionalities (which we call grades). The operators in the geometry change these objects in a covariant ...
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