Visualizing Rotations and Composition of Rotations with Rodrigues' Vector

The purpose of this paper is to show that the mathematical treatment of three dimensional rotations can be simplified, and its geometrical understanding improved, by using the Rodrigues' vector representation. We present a novel geometrical interpretation of the Rodrigues' vector. Based on this interpretation and simple geometrical considerations, we derive Euler Rodrigues' formula, Cayley's rotation formula, and the composition law for finite rotations. The level of this discussion should be suitable for undergraduate physics or engineering courses where rotations are discussed.Comment: 12 pages, 7 figure

Assumptions Underlying Bell's Inequalities

There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of others. The issue, to judge from recent publications, continues to cause misunderstandings. We present a very simple but general proof of Bell's inequalities, identifying explicitly the complete set of assumptions required.Comment: 14 pages. This preprint includes an appendix and some comments not included in the journal version (mainly in section 6), due to length limitations. Comments are welcome