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- Title
Three-Complex Numbers and Related Algebraic Structures.
- Authors
Richter, Wolf-Dieter; Kanel-Belov, Alexei; Planat, Michel
- Abstract
Three-complex numbers are introduced for using a geometric vector product in the three-dimensional Euclidean vector space R 3 and proving its equivalence with a spherical coordinate product. Based upon the definitions of the geometric power and geometric exponential functions, some Euler-type trigonometric representations of three-complex numbers are derived. Further, a general l 2 3 − complex algebraic structure together with its matrix, polynomial and variable basis vector representations are considered. Then, the classes of l p 3 -complex numbers are introduced. As an application, Euler-type formulas are used to construct directional probability laws on the Euclidean unit sphere in R 3 .
- Subjects
SPHERICAL coordinates; VECTOR spaces; POLYNOMIALS; PROBABILITY theory; SPHERES
- Publication
Symmetry (20738994), 2021, Vol 13, Issue 2, p342
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym13020342