On Euler¿s Rotation Theorem

• Tipo: Artigo em Revista Científica Internacional
• Data: 2022

Autores

Gothen, PB (Autor) FCUP; António Guedes de Oliveira (Autor) FCUP

Revista

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Título: College Mathematics Journal

Páginas: 1-6

ISSN: 07468342

Indexação

Scopus - 0 Citações

Outras Informações

ID Authenticus: P-00W-3N7

DOI: 10.1080/07468342.2022.2015214

Abstract (EN): Summary: It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a rigid motion of n-dimensional Euclidean space can be written as the composition of at most n + 1 reflections. The purpose of the present article is, firstly, to present a natural proof of this result in dimension 3 by explicitly constructing a suitable sequence of reflections, and, secondly, to show how a careful analysis of this construction provides a quick and pleasant geometric path to Euler¿s rotation theorem, and to the complete classification of rigid motions of space, whether orientation preserving or not. We believe that our presentation will highlight the elementary nature of the results and hope that readers, perhaps especially those more familiar with the usual linear algebra approach, will appreciate the simplicity and geometric flavor of the arguments.

Idioma: Inglês

Tipo (Avaliação Docente): Científica