Fibonacci Numbers : The Golden Ratio in Nature
 |
| Fibonacci Series |
In 1202, Italian mathematician Leonardo Pisano (also known as Fibonacci, meaning "son of Bonacci") pondered over the question: Given optimal conditions, how many pairs of rabbit can be produced from a single pair of rabbit in one year? This thought experiment dictates that the female rabbits always give birth to pairs, and each pair consists of one male and one female.
Think about it, two new born rabbits are placed in a fenced-in yard and left to breed. Rabbits can't reproduce until they are at least one month old, so for the first month, only one pair remains. At the end of the second month, the female gives birth, leaving two pairs of rabbits. When three roles around, the original pair of rabbits produces yet another pair of new born while their earlier offspring grow to adulthood. This leaves three pairs of rabbit, two of which will give birth to two pairs the following month.
 |
| Fibonacci Series |
The order goes as follows: 1,1,2,3,5,8,13,21,34,55,89,144 and on to infinity. Each number is the sum of the previous two. This series of numbers is known as the Fibonacci numbers or the Fibonacci sequence. The ratio between the numbers (1.618034) is frequently called the golden ratio or golden number.
At first glance, Fibonacci's experiment might seem to offer little beyond the world of speculative rabbit breeding. But the sequence frequently appears in the natural world -- a fact that has intrigued scientists for centuries.
The Golden Ratio in Nature:
Fibonacci numbers appear in nature often enough to prove that they reflect some naturally occurring patterns. You can commonly spot these by studying the manner in which various plants grow. Here are a few examples:
- Seed heads, pinecones, fruits and vegetables:
 |
| Fibonacci Series |
Look at the array of seeds in the center of a sunflower and you will notice what looks like spiral patterns curving left and right. Amazingly, if you count these spirals, your total will be a Fibonacci number. Divide the spirals into those pointed left and right and you'll get two consecutive Fibonacci numbers. You can decipher spiral patterns in pinecones, pineapples and cauliflower that also reflect the Fibonacci sequence in this manner.
 |
| Fibonacci Series |
Some plants express the Fibonacci sequence in their growth points, the places where tree branches form or split. One trunk grows until it produces a branch, resulting in three growth points. Then the trunk and the first branch produce two more growth points. bringing the total to five. This pattern continues, following the Fibonacci numbers. Additionally, if you count the number of petals on a flower. you'll often find the total to be one of the numbers in the Fibonacci sequence. For example, lilies and irises have three petals, buttercups and wild roses have five, delphiniums have eight petals and so on. |
| Fibonacci Series |
A honey bee colony consists of a queen. a few drones and lots of workers. The female bees (queen and workers) all have two parents, a drone and a queen. Drones, on the other hand, hatch from unfertilized eggs. This means they have only one parent. Therefore, Fibonacci numbers express a drone's family tree in that he has one parent, two grandparents, three great-grandparents and so forth. |
| Fibonacci Series |
Take a good look at yourself in the mirror. You'll notice that most of your body parts follow the numbers one, two, three, and five. You have one nose, two eyes, three segments to each limb and five fingers on each hand. The proportions and measurements of the human body can also be divided up in terms of the golden ratio. DNA molecules follow this sequence, measuring 34 angstroms long and 21 angstroms wide for each full cycle of the double helix. Why do so many natural patterns reflect the Fibonacci sequence? Scientists have pondered over the question for centuries. In some cases, the correlation may just be coincidence. In other situations, the ratio exists because that particular growth pattern evolved as the most effective one. In plants, this may mean maximum exposure to light-hungry leaves or maximum seed arrangement.
Comments
Post a Comment
Thanks for visiting my site.