The Fibonacci Sequence are the numbers in the following integer sequence: 1,1,2,3,5,8,13,21,34,55,89,144,... By definition, the first two numbers in the Fibonacci sequence are 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two. The Fibonacci Sequence was first introduced by Fibonacci in his book titled, "Liber Abaci" in 1202. This book introduced the Fibonacci Sequence to western European mathematics. The Fibonacci Sequence is used in many computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. The Fibonacci Sequence also appears in nature often. It appears in the branches of trees, the leafs on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, and many other examples. This sequence is very interesting because it occurs in nature all the time in many different forms, and we don't know why yet. Without the Fibonacci Sequence, we would not have computers or the internet!
The picture above shows the relation between Pascal's Triangle and Fibonacci's sequence.
The Golden Ratio can also be found using the Fibonacci Sequence.