Fibonacci numbers surround us everywhere. They are in music, and in architecture, in poetry, mathematics, economics, in the stock market, in the structure of plants, in the spiral of a snail, in the proportions of the human body and so on, to infinity ...
The famous medieval mathematician Leonardo of Pisa (c. 1170-c. 1250), better known as Fibonacci, was one of the most famous scientists of his time. For the first time in Europe, he proposed using Arabic numbers instead of Roman ones and discovered a mathematical sequence of numbers, later named after him, which looks like this: 1,1,2,3,5,8,13,21, ... and so on to infinity. The sequence of these numbers is sometimes called "Fibonacci numbers."
It is easy to see that in this wonderful sequence, each subsequent number is formed as a result of adding the two previous ones. And why is she wonderful? If we divide each subsequent member of this unique sequence into the previous one, then we will gradually come closer to some amazing transcendental relation - the number (Fibonacci number) = 1.6180339887 ...
This number, like the Pi number (3.1415 ...) does not have an exact value. The number of digits after the decimal point is infinite. This is the beginning of mathematical and not only miracles. If we divide any member of the sequence into the next one, we will also get the transcendental number 0, 6180339887 ... Miracles continue - after the decimal point, the digits exactly repeat the sequence of digits of the number , only before the decimal point is not 1, but 0.
Move on. If we square any Fibonacci number, the result will be the product of the number in the sequence before it, multiplied by the number behind it, plus or minus 1. For example, five squared is 3x8 plus 1; 8 squared is 5x13 minus 1; 13 squared is 8x21 plus 1 and so on. The plus and minus signs change, alternating. There are a great many such mathematical wonders. Fibonacci numbers work wonders around us, we just sometimes don’t notice it.
Fibonacci numbers in nature
Fibonacci ratios, bearing different names - the Golden ratio, the Golden ratio, the Divine proportion - are found in the most unexpected and mysterious places. For example, these ratios can be found with careful consideration of the geometric proportions of the pyramids in Giza, the pyramids in Mexico, the monument of ancient architecture of the Parthenon.
In plants, you can also see this magical relationship. We can again observe the Fibonacci numbers if we carefully consider the inflorescences of various Asteraceae plants: we will find 3 petals in the iris flower, 5 in the primrose, 13 in the ragweed, 34 in the common ravine, and 55 and 89 petals in the aster .
The great Goethe noticed and studied the manifestation of helicity in nature. Spirals can be seen in how the seeds of sunflower, pine cones, cacti, pineapples, etc. are located. In all these cases, the Fibonacci number is manifested. Spider weaves its web in a spiral. Hurricanes spin in a spiral. So galaxies are swirling. “The life curve,” as Johann Goethe called the spiral.
The Fibonacci ratio finds its manifestation in the biology of different organisms. For example, the number of rays of starfish corresponds to Fibonacci numbers. You can also find them in a simple mosquito: he has 3 pairs of legs, 8 segments has an abdomen, and there are 5 antennae on his head. The number of vertebrae in some animals is 55 and so on.
In a lizard, the ratio of the length of its tail to the rest of the body is 62 and 38, and this ratio is harmonious and pleasant for our eyes. In the animal and plant world, symmetry is manifested everywhere. God, Nature or the Great Architect made a division into symmetrical segments, parts and golden proportions. In part, the structure of the whole can be repeated, which is a manifestation of fractality in nature.
Golden symmetry is observed in transitions associated with the energy costs of elementary particles, in the structure of individual chemical compounds, in space systems, in genetic structures, in the structure of certain organs of a person and his body, manifests itself in biorhythms, brain function and perceptual properties.