Search

The article focuses on the use of random tilings to derive a Fibonacci congruence. A tiling of length n has n cells associated with it. To prove that the Fibonacci numbers are given by the Binet formula the calculation of the probability that a random tiling of infinitely many cells using only squares is required. Dominoes is breakable at cell n, that is, a square or a domino begins at cell n, in two different ways. One of the corollaries used involves an application of Euler's theorem. Researchers used different phases for the initial tile and different colors for non-initial tiles.