TL;DR
This paper explores the algebraic structure of paravectors, revealing their geometric properties and similarities to vectors, including concepts like parallelism, perpendicularity, and classical geometric laws.
Contribution
It introduces an integrated product for paravectors, establishing their geometric properties and demonstrating their similarity to vectors in Euclidean geometry.
Findings
Paravectors form a ring structure similar to integers.
The integrated product reveals geometric properties of paravectors.
Paravectors satisfy classical geometric laws like the parallelogram law and Pythagorean theorem.
Abstract
Paravectors just like integers have a ring structure. By introducing an integrated product we get geometric properties which make paravectors similar to vectors. The concepts of parallelism, perpendicularity and the angle are conceptually similar to vector counterparts, known from the Euclidean geometry. Paravectors meet the idea of parallelogram law, Pythagorean theorem and many other properties well-known to everyone.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Micro and Nano Robotics