Fibonacci numbers are all around us.They're in music, in architecture, in poetry, mathematics, economics, the stock market, in the structure of plants in the cochlear spiral, in the proportions of the human body and so on, to infinity ...
Famous medieval mathematician Leonardo of Pisa (c. 1170-tuples. 1250), better known as Fibonacci, was one of the most famous scientists of his time.He was the first in Europe suggested using Arabic numerals instead of Roman and opened a mathematical sequence of numbers, later named after him, which is as follows: 1,1,2,3,5,8,13,21, ... and so on to infinity.The sequence of these numbers is sometimes called the "Fibonacci numbers".
easy to notice that in the remarkable sequence of each successive number is formed by adding the two previous ones.And what is it remarkable?If we divide each additional member of this unique sequence of the previous one, then we will gradually approach to some amazing transcendental ratio - the number of F (Fibonacci number) = 1,6180339887 ...
This number, like the number pi (3.1415 ...) has no precisevalues.The number of digits after the decimal point is infinite.This is the beginning and not just mathematical miracles.If we divide each term of the sequence for the following, we also obtain a transcendental number 0 6180339887 ... Miracles continues - after the decimal digits repeat exactly the sequence of digits of F, not only to point 1, and 0.
Go ahead.If we square the any Fibonacci number, the result will be equal to the number of standing in the sequence in front of him, multiplied by the number that is behind it, plus or minus 1. For example, five squared equals 3x8 + 1;8 squared is equal to minus 1 5x13;13, erected in the square, equal to 8x21 + 1 and so on."Plus" and "minus" change alternately.Such mathematical miracles here in abundance.Fibonacci numbers work wonders around us, but we sometimes do not notice.
Fibonacci numbers in nature
Fibonacci ratios, bearing different names - Golden proportion, golden section, divine proportion - are found in the most unexpected and mysterious places.For example, the ratio can be found on closer examination the geometric proportions of the pyramids of Giza, the pyramids in Mexico, the monument of ancient architecture of the Parthenon.
In plants, you can also see a magical relationship.Fibonacci numbers we can observe again, if we carefully consider the various blossoms Asteraceae plant: the flower iris petal 3 we find, at the Primrose - 5, at the ragweed - 13, Leucanthemum vulgare at -34, while the aster - 55 and 89 petals.
great Goethe observed and studied the expression of helicity in nature.Spirals can be seen in the way arranged sunflower seeds, pine cones, in cacti, pineapples and others. In all these cases appears Fibonacci number.Spiral spider weaves its web.Hurricanes twisted spiral.So twisted and galaxies."The curve of life" - the so-called spiral Johann Goethe.
is manifested Fibonacci ratio and biology of various organisms.For example, the number of rays starfish correspond to Fibonacci numbers.A simple mosquito can also find them: the legs had three couples, 8 segments has a belly, and on his head there is a 5 antennae.The number of vertebrae in some animals is 55 and so on.
lizard ratio of the length of its tail to the rest of the body length of 62 and 38, and the proportion is harmonious and pleasing to our eyes.The flora and fauna everywhere evident symmetry.God, the Great Architect of Nature, or carried out the division into symmetrical segments, parts and golden proportion.As part of the whole structure can be repeated, which is a manifestation of fractal in nature.
Gold symmetry observed in the transitions associated with the energy consumption of elementary particles in the structure of certain chemical compounds in space systems, in genetic structure, in the structure of certain organs and body is manifested in biorhythms, brain function and properties of perception.
