Self-Reverse Elements and Lines in an Algebra for 3D Space

A geometric algebra provides a single environment in which geometric entities can be represented and manipulated and in which transforms can be applied to these entities. A number of versions of geometric algebra have been proposed and the aim of the paper is to investigate one of these as it has a...

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Bibliographic Details
Published in:Advances in applied Clifford algebras 2020-09, Vol.30 (4), Article 50
Main Authors: Cripps, Robert J., Cross, Ben, Mullineux, Glen
Format: Article
Language:English
Subjects:
Algebra
Applications of Mathematics
Equivalence
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Theoretical
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Summary:A geometric algebra provides a single environment in which geometric entities can be represented and manipulated and in which transforms can be applied to these entities. A number of versions of geometric algebra have been proposed and the aim of the paper is to investigate one of these as it has a number of advantageous features. Points, lines and planes are presented naturally by element of grades 1, 2, and 3 respectively. The self-reverse elements in the algebra form a field. This allows an equivalence relation between elements of grade 2 to be defined so that, although not every grade 2 element corresponds to a line, each equivalence class does, and vice versa. Examples are given to illustrate the ease in which geometric objects are represented and manipulated.
ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-020-01075-7