Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T06:12:27.116Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Random Disorientation of two Cubes

Published online by Cambridge University Press:  20 November 2018

D. C. Handscomb
D. C. Handscomb*
Affiliation:
Christ Church, Oxford
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We are given two identical symmetrical bodies (e.g., cubes) with independent random orientations; then we can always, in several ways, turn one of these bodies about some axis through its centre of gravity, so as to bring it into the same orientation as the other body. The smallest angle of rotation needed will be called the disorientation, d, of the two bodies, and we shall be concerned with the distribution of d under these conditions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 10 , 1958 , pp. 85 - 88
Copyright
Copyright © Canadian Mathematical Society 1958

References

1. Ball, W. W. R., Mathematical Recreations and Essays (11th ed., London, 1939).Google Scholar
2. Coxeter, H. S. M., The binary polyhedral groups … , Duke Math. J., 7 (1940), 367-379.Google Scholar
3. Coxeter, H. S. M. Regular Polytopes (London, 1948).Google Scholar
4. Coxeter, H. S. M. Regular honeycombs in elliptic space, Proc. Lond. Math. Soc. (3), 4 (1954), 471-501.Google Scholar
5. Delthiel, R., Probabilités Géométriques, Tome 2, Fasc. 2 of E. Borel, Traité du Calcul des Probabilités … (Paris, 1926).Google Scholar
6. Mackenzie, J. K. and Thomson, M. J., Some statistics associated with the random disorientation of cubes, Biometrika, 44(1957), 205-210.Google Scholar
7. Robinson, G. de B., On the orthogonal groups in four dimensions, Proc. Camb. Phil. Soc, 27 (1931), 37-48.Google Scholar