From Vectors to Geometric Algebra
General Mathematics
2018-02-23 v1
Abstract
Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous Pythagorean theorem. Synthetic proofs of theorems in Euclidean geometry can then be replaced by powerful algebraic proofs. Whereas we largely limit our attention to 2 and 3 dimensions, geometric algebra is applicable in any number of dimensions, and in both Euclidean and non-Euclidean geometries.
Cite
@article{arxiv.1802.08153,
title = {From Vectors to Geometric Algebra},
author = {Sergio Ramos Ramirez and Jose Alfonso Juarez Gonzalez and Garret Sobczyk},
journal= {arXiv preprint arXiv:1802.08153},
year = {2018}
}
Comments
26 pages, 23 figures, also available in Spanish