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Cubes

Feature Column Archive

8. References

Beck, A. and M. Bleicher, and D. Crowe, Excursions into Mathematics, Millennium Edition, A K Peters, Natick, 2000.

Coxeter, H., Regular Polytopes, Third Edition, Dover, New York, 1973.

Crowe, D., The n-dimensional cube and the Tower of Hanoi, Amer. Math. Monthly, 63 (1956) 29-30.

Dixon, E. and S. Goodman, On the number of Hamiltonian circuits in the n-cube, Pro. AMS, 50 (1975) 500-504.

Gardner, M., The Scientific American Book of Mathematical Puzzles and Diversions, Simon and Schuster, New York, 1959.

Gardner, M., The 2nd Scientific American Book of Puzzles and Diversions, Simon and Schuster, New York, 1961

Gardner, M., Mathematical Carnival, Alfred Knopf, New York, 1975.

Klee, V. and G. Minty, How Good is the Simplex Algorithm?, in Inequalities III, O. Shinsha (ed.), Academic Press, New York, 1972.

Manning, H., The Fourth Dimension Simply Explained, Dover, New York, 1960.

Mills, W., Some complete cycles on the n-cube, Proc. AMS, 14 (1963) 640-643.

Sommerville, D., An Introduction to the Geometry of N Dimensions, Dover, New York, 1958.

Steele, J., Shortest paths through pseudo-random points in the d-cube, Proc. AMS, 80 (1980) 130-134.

Those who can access JSTOR can find some of the papers mentioned above there. For those with access, the American Mathematical Society's MathSciNet can be used to get additional bibliographic information and reviews of some of these materials.

  1. Introduction
  2. Some history
  3. The 3-dimensional cube
  4. Combinatorial perspectives on cubes
  5. A recursive way of constructing cubes
  6. Cube puzzles
  7. Symmetries of the cube
  8. The Sharir-Ziegler cube
  9. References