The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ... (add the last two to get the next) The lengths are identical to the lengths first shown, this proves that the section’s of a human increase by a 1.618 ratio or phi. Look at your hand, the ratio of your forearm to your hand is also phi. pattern of: 1, 2, 3, 5, 8, 13, 21, 34 and so on. This is a clear example of the Fibonacci sequence starting at 1. Why in nature, do most flowers have a Fibonacci number of petals? look at a sunflower head. When you look at the head you notice two series of curves one winding in one sense and one in another; the number of spirals not being the same in each sense. Why is the number of spirals in general either 21 and 34, either 34 and 55, either 55 and 89, or 89 and 144? They all belong to the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, but the explanation is also linked to another famous number, the golden mean. In many cases, the head of a flower is made up of small seeds which are produced at the center, and then migrate towards the outside to fill eventually all the space (as for the sunflower but on a much smaller level). Each new seed appears at a certain angle in relation to the preceding one. For example, if the angle is 90 degrees, that is 1/4 of a turn, the result after several generations is four straight lines starting from the center in a 90 degree angle. Of course, this is not the most efficient way of filling space. In fact, if the angle between the appearance of each seed is a portion of a turn which corresponds to a simple fraction, 1/3, 1/4, 3/4, 2/5, 3/7, etc (that is a simple rational number), one always obtains a series of straight lines. If you want to get a spiral, it is necessary to choose a portion of the circle which is an irrational number (or a non simple fraction). If this latter is well approximated by a simple fraction, one obtains a series of curved lines (spiral arms) which even then do not fill out the space perfectly. In order to optimize the filling, it is necessary to choose the most irrational number there is, that is to say, the one the least well approximated by a fraction. This number is exactly the golden mean. The corresponding angle, the golden angle, is 137.5 degrees. (It is obtained by multiplying the non-whole part of the golden mean by 360 degrees and, since one obtains an angle greater than 180 degrees, by taking its complement). With this angle, one obtains the optimal filling, that is, the same spacing between all the seeds (see sunflower head). When the angle is exactly the golden mean, and only this one, two families of spirals (one in each direction) are then visible: their numbers correspond to the numerator and denominator of one of the fractions which approximates the golden mean : 2/3, 3/5, 5/8, 8/13, 13/21, etc.These numbers are precisely those of the Fibonacci sequence (the bigger the numbers, the better the approximation) and the choice of the fraction depends on the time laps between the appearance of each of the seeds at the center of the flower. This is why the number of spirals in the centers of sunflowers, and in the centers of flowers in general, correspond to a Fibonacci number. Moreover, generally the petals of flowers are formed at the extremity of one of the families of spiral. This then is also why the number of petals corresponds on average to a Fibonacci number. However, you can also find the Fibonacci sequence starting on 13 through just ordinary field daisies. There are daisies with 13, 21, 34, 55 and even 89 petals; these are all prime examples of the Fibonacci sequence. Although petal number is intriguing, if one looked even closer into the stems of a simple plant, you could also find the pronounced Fibonacci sequence. If you draw lines through the flower’s axils, you’ll see that the number of branches up each level represent the Fibonacci number sequence Many plants show the Fibonacci numbers in the arrangement of the leaves around the stem. Some pine cones and fir cones also show the numbers, as do daisies and sunflowers. Sunflowers can contain the number 89, or even 144. Many other plants, such as succulents, also show the numbers. Some coniferous trees show these numbers in the bumps on their trunks. And palm trees show the numbers in the rings on their trunks. Fibonacci numbers or patterns are found in: Sea Shells, Petals on Flowers, Sunflower seed Heads, Pine Cones, Palms, Pineapple and other Bromeliads, and Plant Growth or leaf/petal arrangements in 90% of plants.Probably most of us have never taken the time to examine very carefully the number or arrangement of petals on a flower. The number of leaves up each level, also represents the Fibonacci Sequence! The Fibonacci pattern also occurs in tree growth with the number of branches from bottom to top in trees. pineapple, its scales are also patterned into 3 distinct spirals: 5, 8, and 13 Our Milky Way even has the Fibonacci spiral imbedded into it. As shown previously in the explanation of the Golden Ratio, the following spiral can be obtained using the Fibonacci sequence. The Mona Lisa, indisputably Leonardos most famous painting, is full of Golden Rectangles. If you draw a rectangle whose base extends from the womans right wrist to her left elbow and extend the rectangle vertically until it reaches the very top of her head, you will have a Golden Rectangle. A golden rectangle is a rectangle whose side lengths are in the golden ratio, 1: j (one-to-phi), that is, 1 : or approximately 1:1.618. In finance, Fibonacci retracement is a method of technical analysis for determining support and resistance levels. They are named after their use of the Fibonacci sequence. Fibonacci retracement is based on the idea that markets will retrace a predictable portion of a move, after which they will continue to move in the original direction. Source:fabulousfibonacci/ scienceline.ucsb.edu/getkey.php?key=111 en.wikipedia.org/wiki/Fibonacci_retracement
Posted on: Sat, 26 Jul 2014 14:08:02 +0000
Trending Topics
Recently Viewed Topics
© 2015