# Collection of places where Fibonacci numbers appear

A single newly born pair of rabbits (one male, one female) are put in a field. These rabbits are able to mate at the age of one month, so that at the end of its second month, a female can produce another pair of rabbits. These rabbits never die, and a mating pair always produces one new pair (one male, one female) every month from the second month on. The number of pairs of rabbits, in the nth month, is \(F_n.\)

If I am going up n stairs, taking 1 or 2 steps at a time, the number of ways I can go up the stairs is \(F_n.\)

The number of ways to tile an 2xn grid with 2x1 dominoes, is \(F_n.\)

The sum of certain diagonals of Pascal's triangle, yield Fibonacci numbers: