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On the mobility of bodies in ℝn

Published online by Cambridge University Press:  24 October 2008

R. J. MacG. Dawson
R. J. MacG. Dawson
Affiliation:
Corpus Christi College, Cambridge CB2 1RH
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Extract

We may define a mobility problem to be one of the type: ‘Given a (fully or partlys pecified) collection of bodies in ℝn, assumed not to interpenetrate, can they be moved in some (fully or partly specified) fashion?’ Early examples of mobility problems nclude ‘Chinese puzzles’ and Sam Loyd's ‘15 puzzle’ (to which could be added the more recent Rubik's Cube!) Less combinatorial examples include the ‘piano mover’ problem (see, e.g. [2, 3, 9]) and the several recent papers on collision avoidance, such as [1, 5, 6, 7, 8].

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 3 , November 1985 , pp. 403 - 412
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Dawson, R. J. MacG.. On removing a ball without disturbing the others. Mathematics Magazine 57 (1984), 27–30.Google Scholar
[2]Guy, R. K.. Monthly research problems. Amer. Math. Monthly 84 (1977), 811.Google Scholar
[3]Moser, L.. Problem 66–11. SIAM Rev. 8 (1966), 381.CrossRefGoogle Scholar
[4]Pontryagin, L. S.. Topological Groups. (Gordon and Breach, 1966).Google Scholar
[5]Toussaint, G. T. and Sack, J.-R.. Some new results on moving polygons in the plane. Proc. Robotic Intelligence and Productivity Conference (Detroit, Michigan, 1983), 158–163.Google Scholar
[6]Toussaint, G. T.. On Translating a Set of Spheres. Tech. Report SOCS 84.4, School of Computer Science (McGill University, 1984).Google Scholar
[7]Toussaint, G. T.. On Translating a Set of Polyhedia. Conference on Polyhedra (Smith College, 1984).Google Scholar
[8]Toussaint, G. T. and ElGindy, H. A.. Two Monotone Polygons can be Separated in Linear Time. Tech. Report SOCS 84·7 (School of Computer Science, McGill University, 1984).Google Scholar
[9]Wagner, N. R. The sofa problem. Amer. Math. Monthly 83 (1976), 188–189.Google Scholar