Domino

$\begin{figure}\begin{center}\BoxedEPSF{Domino.epsf scaled 1000}\end{center}\end{figure}$

The unique 2-Polyomino consisting of two equal squares connected along a complete Edge.

The Fibonacci Number $F_{n+1}$ gives the number of ways for $2\times 1$ dominoes to cover a $2\times n$ Checkerboard, as illustrated in the following diagrams (Dickau).

$\begin{figure}\begin{center}\BoxedEPSF{FibonacciChecker3.epsf}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{FibonacciChecker4.epsf}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{FibonacciChecker5.epsf}\end{center}\end{figure}$

References

Dickau, R. M. ``Fibonacci Numbers.'' http://www.prairienet.org/~pops/fibboard.html.

Gardner, M. ``Polyominoes.'' Ch. 13 in The Scientific American Book of Mathematical Puzzles & Diversions. New York: Simon and Schuster, pp. 124-140, 1959.

Kraitchik, M. ``Dominoes.'' §12.1.22 in Mathematical Recreations. New York: W. W. Norton, pp. 298-302, 1942.

Lei, A. ``Domino.'' http://www.cs.ust.hk/~philipl/omino/domino.html.

Madachy, J. S. ``Domino Recreations.'' Madachy's Mathematical Recreations. New York: Dover, pp. 209-219, 1979.