Nature's perfect creation, convinced scientists that reveal the structure of the human body the proportions of the Golden section, and the head of cauliflower is a fractal figure.
"Study and observation of nature gave birth to science," wrote Cicero in the first century BC. In more recent times with the development of science and distancing it from the study of nature, scientists are surprised to discover that was known to our ancestors, but was not confirmed by scientific methods.
Interesting to find a similar education in micro - and macrocosm, can be an inspiration and the fact that the geometry of these entities science can describe. Circulatory system, river, lightning, tree branches, this is a similar system consisting of different particles and different in scale.
Sacred geometry involves sacred universal patterns used to build all things in our reality. Most often seen in sacred architecture and art. There is also the knowledge that geometry and mathematical ratios, harmonics and proportion are found in music, light, cosmology.
Music. Discoveries in the field of music, revealing its relation to geometry and mathematics made in the classical period, is attributed to Pythagoras. He found that the octave peculiar to the ratio of 2:1, the ratio 3:2 characterizes the fifth, and 4:3 – quart. The Pythagoreans believed that this ratio gave music powers of healing, able to harmonize the unbalanced body, and this belief has been revived in modern times. Hans Jenny, a physicist, a founder of the science of cymatics, the study of the influence of acoustic vibrations on geometric shapes (Hans Jenny Cymatics: A Study of Wave Phenomena & Vibration. — 3rd. — Macromedia Press, 2001), often cited in this context.
As an example of building a violin based on the Golden section, take the violin of Antonio Stradivari made in 1700
The proportions of "Golden section"
The Golden ratio, known as the God ratio, Golden proportion, Golden mean, Golden number, divine proportion or sectio divina, is an irrational number that equals 1.618 033 988 749 894 848, possessing interesting properties. Forms that had proportions according to the Golden section in Western culture has long been considered the most pleasing to the eye. The Golden ratio is still used frequently in art and design, suggesting a natural balance between symmetry and asymmetry.
If you build a rectangle with sides the ratio of which is equal to the proportion of "Golden section" and insert another "Golden rectangle", that is another, and so on to infinity inside and outside, at the corner points of the rectangles it is possible to hold the spiral. The interesting thing is that this spiral will coincide with the slice of the shell of the Nautilus and other naturally occurring spirals.
The Fossil Nautilus. Photo: Studio-Annika/Photos.com
The Shell Of The Nautilus. Photo: Chris 73/en.wikipedia.org
The proportion of the Golden section is perceived by the human eye as a beautiful, harmonious. And the ratio of 0.618... is the ratio of the previous to the next number in the Fibonacci series. The number of Fibonacci series is everywhere manifest in nature: it is a spiral, in which branches of plants adjacent to the stem, the spiral, which grows scales on the lump or grain sunflower. Interestingly, the number of rows, twisting counter-clockwise and clockwise is neighboring numbers in the Fibonacci series.
Spiral curls head of broccoli and a RAM's horn... and in the human body, of course, healthy and normal proportions, are ratios of the Golden section.
Vitruvian man. The figure of Leonardo da Vinci.
1, 1, 2, 3, 5, 8, 13, 21, ... — the number of Fibonacci series in which each subsequent term is derived from the sum of the previous two. Distant spiral galaxy captured satellites, also twisted in spirals, Fibonacci.
A spiral galaxy. Photo: NASA
Three tropical cyclone. Photo: NASA
Twisted helix of human DNA. Illustration: Zephyris/en.wikipedia.org
Spiral spins its web spider.
The web spider. Photo: Vincent de Groot/videgro.net
Aloe Polyphylla
Sunflower
The "Golden ratio" can be seen in the structure of the body of the butterfly in relation to thoracic and abdominal parts of her calf, and also dragonflies. And most of the eggs if you don't fit in the Golden rectangle, is derived from him.
Fractals
Other interesting figures which we can everywhere see in nature are fractals. Fractals are shapes made up of parts, each of which is similar to a figure — does not this remind the principle of the Golden section?
Trees, lightning, bronchi and human circulatory system have a fractal shape, perfect natural illustrations of fractals referred to as ferns and broccoli. "Everything is so difficult, so simple" the way of nature, notice the people with respect by listening to her.
"Nature has endowed man with a desire for finding the truth," wrote Cicero, words which I would like to finish the first part of the article on geometry in nature.
Broccoli — a perfect illustration of a natural fractal. Photo: pdphoto.org
Fern leaves have the form of fractal shapes — they are self-similar. Photo: Stockbyte/Photos.com
The cracked stone: a fractal in the macro. Photo: Bob Beale/Photos.com
Branching of the circulatory system on the rabbit ears. Photo: Lusoimages/Photos.com
Lightning — branch fractal. Photo: John R. Southern/flickr.com
Branch of arteries in the human body. Photo: Jupiterimages/Photos.com
Winding river and its branches. Photo: Jupiterimages/Photos.com
Ice frozen on the glass has the self-similar pattern. Photo: Schnobby/en.wikipedia.org
The ivy leaf with branching veins — fractal form. Photo: Wojciech Plonka/Photos.com
Tree branches without leaves resemble the branching of veins on a leaf. Natural fractal. Photo: Spencer Smith/Photos.com
source:epochtimes.com.ua/ru; you-journal.ru
Enjoyed.
http://www.biogeometry.org/page22.html might be of interest to you.
Thank you.
Interesting... I have a mathematical intuition which aims to consider any organic body as a Remannian 3nd Order Manifold, and then mixed it with physics Minimal Action Principile. The idea behind is trying to formalize why Nature is always beautiful in its multiple manifests..
you may find interesting my post where I have made a study of these gorgeous girls drawn by Milo Manara. He uses a PHI algorithm!