# Equivalence of Two Fibonacci Number Interpretations

Equivalence of Two Fibonacci Number Interpretations

This Demonstration illustrates the equivalence of these two interpretations of the Fibonacci numbers :

F

n

• the number of ways to tile a checkerboard with dominoes• the number of ways a ray of light can pass through two panes of glass with reflections

2×(n-1)

2×1

(n-1)

In the figure, when viewing reflections, the top row of the checkerboard pattern represents one pane of glass, and the bottom row represents the second pane of glass; reflections can occur on any of the three "surfaces" of the panes.