Domino (mathematics)
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In mathematics, a domino is a polyomino of order 2, that is, a polygon in the plane made of two equal-sized squares connected edge-to-edge,[1] and a 1x2 rectangle. [2] When rotations and reflections are not considered to be distinct shapes, there is only one 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°.[3][4]
In a wider sense, the term domino is sometimes understood to mean a tile of any shape.[5]
Packing and tiling
Template:Main 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.[6]
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,[7] 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.[8]
See also
References
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- ↑ Just Look at it!
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- ↑ Concrete Mathematics Template:Webarchive by Graham, Knuth and Patashnik, Addison-Wesley, 1994, p. 320, Template:ISBN
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