The Golden Ratio and Fibonacci Numbers in Nature. Fibonacci numbers. By: Mary Catherine Clark. Leonardo Fibonacci was the most outstanding mathematician of the European Middle Ages. He was known by other names including Leonardo Pisano or Leonard of Pisa.
Leonardo Fibonacci was the most outstanding mathematician of the European Middle Ages.
He employed algebra to solve geometric problems and geometry to solve algebraic problems. This was radical in Europe at the time.
He wrote two other books. One of which included Liber Quadratorum. This earned him the reputation as a major number theorist.History cont.
He was one of the first people to introduce the Hindu-Arabic number system to Europe- the system used today.
The sequence in which each number is the sum of the two preceding numbers.
Fibonacci’s book LiberAbcai asked a question involving the reproduction of a single pair of rabbits which is the basis of the Fibonacci sequence.
Answer: 144 rabbits
The golden rectangle can be constructed from these line segment so that the length to width ratio is φ.
The ratio of successive Fibonacci numbers is something you might be surprised by!
As n increases, the ratio of approaches the golden ratio and is expressed as =
This is the fundamental property of both the Fibonacci sequence and the golden ratio.
Both of these ratios converge at the same limit and are the positive root of the quadratic equationWhat does this have to do with fibonacci numbers?
If the two smallest squares have a width and height of 1, then the box to their left has a measurement of 2 and the other boxes measure 3, 5, 8, and 13.
Look at any seed head, and you will notice what look like spiral patterns curving out form the center left and right.Fibonacci numbers in nature
If you count these spirals you will find a Fibonacci number. If you look at the spirals to the left and then the right you will notices these are two consecutive Fibonacci numbers.
Most of the time, the number of pedals on a flower is a Fibonacci number!More fibonacci numbers in nature
1 pedal-calla lily
13 pedals-black eyed susan
Dunlap, Richard A. The Golden Ratio and Fibonacci Numbers. Singapore: World Scientific, 1997.
Koshy, Thomas. Fibonacci and Lucas Numbers with Applications. New York: John Wiley & Sons, inc., 2001.
Vorobiev, Nicolai N. Fibonacci Numbers. 6th. Basel: Birkhauser Verlag, 1992.Works cited