The Fibonacci Series can be seen in the number of petals on a sunflower.

The Fibonacci Series is a sequence of numbers that has been a focus of mathematical thought for over 700 years. Attributed to the Italian mathematician Leonardo Fibonacci (c. 1170-c. 1250), the series can be found occurring frequently in nature and shares a connection to other mathematical concepts, particularly the Golden Ratio. Today, mathematicians continue to study the Fibonacci Series, continuously adding to the applications of this number theory.

## History

The Fibonacci Series was first discovered by Leonardo Fibonacci in 1202. In his work “Liber Abaci,” the Italian mathematician created a problem designed to calculate the multiplication rate of rabbits. Starting out with a single pair, he created a number sequence that determined the rate of increase a rabbit population would experience over time in an ideal set of conditions. This sequence became the Fibonacci Series.

## Explanation

The *Fibonacci Series* is a simple set of numbers, operating under the idea that each pair of numbers in the sequence can be added to create the next number in the sequence. For example, the first two numbers in the sequence are 1 and 1. Added together, the next number is 2, followed by 3, 5, 8, 11. Any two consecutive numbers in the sequence must equal the **next number** when added in order to be Fibonacci numbers.

## Real-World Presence

The Fibonacci Series occurs frequently throughout nature. Certain flowers, such as sunflowers and daisies are most commonly found featuring petal counts in numbers that occur in the Series. Pineapples, pine cones and other seed heads feature spirals that correspond to **Fibonacci numbers**. The Fibonacci Series occurs in the number of pitches per octave in music and has even been utilized when creating betting systems for roulette.

## Relation to Golden Mean

The Fibonacci Series bears a direct connection to the Golden Ratio. Found in plants, living organisms and man-made designs, the **Golden Ratio** is 1.618. As numbers in the Fibonacci Series increase, the divided ratio of any two consecutive numbers eventually reaches and stabilizes at 1.618. The Golden Rectangle, claimed to be the most aesthetically pleasing rectangle when discovered by Pythagoras, contains the ratio of 1.618 when you divide the length by the height.