From Vectors to Geometric Algebra

Por • 1 mar, 2018 • Sección: Ambiente

Sergio Ramos Ramirez, Jose Alfonso Juarez Gonzalez, Garret Sobczyk

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.

arXiv:1802.08153v1 [math.GM]

General Mathematics (math.GM)

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