Fibonacci Numbers
By: Fabian Meraz
A bit of History
When you hear the name Fibonacci, you probably think of the Fibonacci sequence. Fibonacci did not actually coin the term "Fibonacci numbers." Edouard Lucas, a nineteenth century number theorist, actually gave the Fibonacci sequence its name. Why would he do this? Well, Lucas did this because Fibonacci gave the following problem ""A certain man put a pair of rabbits in a place surrounded by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair from which the second month on becomes productive?" This gives the sequence 1,1,2,3,5,8..... The Fibonacci Sequence!
What are the Fibonacci numbers?
The Fibonacci numbers are 0,1,1,2,3,5,8,..... How do we get each number? To get the next Fibonacci number, we simply add the two numbers that are before it.
Okay, the previous formula works but what if we don't know the two previous Fibonacci numbers? There is a formula for the nth Fibonacci number that does not require for you to know the previous Fibonacci number. This formula is called Binet's formula.
This sequence is Everywhere!
The Fibonacci sequence can actually be found in nature. This video does an excellent job of showing this (and it is more fun to see it than to just read about it). The video should automatically start at 01:11.
Test question:
Use the both the recursive equation and Binet's formula to find the 10th Fibonacci number.
Very random fact:
My birthday is 11/23 and my brother's birthday is 5/8. If we put these numbers together we get 1,1,2,3,5,8.....Spooky.
Sources:
Discrete Math Arthur T. Benjamin
The History of Mathematics by David M. Burton