After revising recognized representations of the gang of Euclidean displacements Daniel Klawitter provides a complete creation into Clifford algebras. The Clifford algebra calculus is used to build new types that permit descriptions of the gang of projective differences and inversions with admire to hyperquadrics. Afterwards, chain geometries over Clifford algebras and their subchain geometries are tested. the writer applies this concept and the constructed easy methods to the homogeneous Clifford algebra version reminiscent of Euclidean geometry. furthermore, kinematic mappings for distinct Cayley-Klein geometries are constructed. those mappings enable an outline of current kinematic mappings in a unifying framework.

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