A Geometric Interpretation of the Simplicity of SO(3)

Abstract

This article aims to present a geometric interpretation of the simplicity of the rotation group of three-dimensional Euclidean space. Some historical remarks on the subject and an overview of a collection of different proofs of this result are also given.

• MSC: Primary 51F25
• Secondary 20E32
• 15B10
• 22C05
• 11R52

Acknowledgments

The author expresses his gratitude to the anonymous referees for insightful comments and judicious suggestions and criticisms that have resulted in substantial improvements to the manuscript, to the editors of this Monthly for constructive comments and suggestions and generous editorial assistance, and to E. Ben-David, M. Ghebleh, A. B. Hushmandi and M. Nouri-Moghadam for generous help in reading and suggesting corrections to the manuscript. Support from Sharif University of Technology is acknowledged.

Notes

1 In particular, the real closure of an ordered field $(F,\le )$ with a non-Archimedean ordering is always Euclidean. Roughly speaking, the real closure of $(F,\le )$ is the largest algebraic ordered extension of $(F,\le )$.

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Notes on contributors

M. G. Mahmoudi

MOHAMMAD G. MAHMOUDI received his B.Sc and M.Sc in 1997 and 1999, respectively, from Sharif University of Technology, Iran and his Ph.D. in 2004 from the University of Franche-Comté, France. He is an assistant professor of mathematics at Sharif University of Technology, Iran.