Domino (mathematics)

Source: Wikipedia, the free encyclopedia.
This article is about the mathematical polygon. For the game, see dominoes.
The single free domino

In mathematics, a domino is a

free
domino.

Since it has reflection symmetry, it is also the only one-sided domino (with reflections considered distinct). When rotations are also considered distinct, there are two fixed dominoes: The second one can be created by rotating the one above by 90°.[2][3]

In a wider sense, the term domino is sometimes understood to mean a tile of any shape.[4]

Packing and tiling

Main article: Domino tiling

Dominos can tile the plane in a countably infinite number of ways. The number of tilings of a 2×n rectangle with dominoes is , the nth

Fibonacci number.[5]

Domino tilings figure in several celebrated problems, including the Aztec diamond problem in which large diamond-shaped regions have a number of tilings equal to a power of two,[6] with most tilings appearing random within a central circular region and having a more regular structure outside of this "arctic circle", and the mutilated chessboard problem, in which removing two opposite corners from a chessboard makes it impossible to tile with dominoes.[7]

See also

  • Dominoes, a set of domino-shaped gaming pieces
  • Tatami, Japanese domino-shaped floor mats

References

  1. ISBN 0-691-02444-8
    .
  2. ^ Weisstein, Eric W. "Domino". From MathWorld – A Wolfram Web Resource. Retrieved 2009-12-05.
  3. doi:10.1016/0012-365X(81)90237-5
    .
  4. ^ Berger, Robert (1966). "The undecidability of the Domino Problem". Memoirs Am. Math. Soc. 66.
  5. ISBN 0-201-55802-5
  6. MR 1226347
  7. JSTOR 4146865
    .
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