Golden tulle in Vikonal roslins: Kolchina L.A. Golden border and symmetry Apply a golden border on the ground

Biological studies have 70-90 years. it is shown that, beginning with viruses and roslin and ending with the human body, everywhere there is a gold proportion, which characterizes the proportion and harmony of the life. The golden edge is recognized by the universal law of living systems. It is possible to distinguish two types of manifestations of the golden edge in living nature: irrational blue for Pythagoras - 1.62 and qlimi, discrete - for Fibonacci.

It was established that the number of Fibonacci numbers characterizes the structural organization of rich living systems. For example, twine leaf mashing on the gіltsі to become drіb (number of wrappers on the stem/number of leaves in the cycle, for example 2/5; 3/8; 5/13), which matches the Fibonacci rows. Kindly see the "gold" proportion of five-pellet flowers of apple trees, pears and riches of other trees. Carrying the genetic code - DNA and RNA molecules - shaping the structure of the helix; її razmіri mayzhe povnistyu vіdpovіdat numbers of the Fibonacci series.

Sche Goethe blatantly on the tendencies of nature to spiralness. A spider weaves a cobweb spirally. A hurricane is spinning in a spiral. The green herd of deer deer grows in a spiral. The DNA molecule is twisted in an underwire spiral. Goethe naming the spiral "crooked life". Gvintopodіbne and spiral-like roztashuvannya leaves on the tree trunks were commemorated long ago. The spiral was sipped at the rosemary of the dormouse plant, at the pine cones, pineapples, and cacti. The joint work of botanists and mathematicians shed light on the wondrous natural phenomena. It was clear that in the roztashuvanni leafing on the gіltsі (phylotaxis), on the dormouse tree, the pine cone reveals a series of Fibonacci, and also, reveals the law of the golden peretina. Flowers and flowers of dormouse, chamomile, litter in pineapple fruits, coniferous cones are "packed" behind logarithmic ("golden") spirals, which curl one to one, moreover, the numbers of "right" and "left" spirals are always seen one to one, like sucrose Fibonacci numbers.

Let's respectfully wait until the chicory flows. Vіd the main stalk utvilis vіdrostok. Immediately, the first leaf was rotting. The second is to break a strong wikid in the open, zupinyaetsya, let out a leaf, but it is shorter than the first one, again to break the wikid in the open, but even less strength, let out a leaf of an even smaller size and renew the wikid.

If the first wikid is taken as 100 ones, the other one is equal to 62 ones, the third one is 38, the fourth one is 24 and so on. Dovzhina pelyustok also under the order of the golden proportions. In the growing country, conquered by the expanse, the growth took the same proportions. The impulses of this growth step by step changed in proportion to the golden border.

In rich panicles, the expansion of the chest and the cranial part of the body is in golden proportion. Having folded the krill, the night blizzard establishes the correct equal-sided tricot. Ale varto spread the krill, and you will follow the very principle of articulation of the body at 2,3,5,8. The grandmother is also created according to the laws of golden proportions: the extension of the length of the tail and the hull of the body are extended the length of the crown to the length of the tail.

The lizards at first glance catch the proportions for our eye - the length of the tail should lie down to the length of the body, like 62 to 38.

And in the dewy, and in the creaturely world, the formative tendency of nature is blatantly breaking through - the symmetry of how directly grows that rush. Here, the golden veneer appears in the proportions of the parts perpendicularly to a straight line.

Nature created a podil on symmetrical parts and golden proportions. The parts show a repetition of the life of the whole

The great Goethe, sings, naturalist and artist (wine painting and painting watercolors), dreaming about the creation of a single idea about the form, illuminating that transformation of organic bodies. Tse vіn vvіv u svekoviy uzhitek termіn morfologiya.

P'єr Cury on the cob of our century, having formulated low deep ideas of symmetry. Vіn stverdzhuvav, scho it is impossible to see the symmetry of such a body, not vrahovoyuchi symmetry of the superfluous middle.

The laws of "golden" symmetry are manifested in the energy transitions of elementary particles, in everyday chemical fields, in planetary and cosmic systems, in the genetic structures of living organisms. The number of regularities, as it is designated more, is in the life of the human body and the body in general, as well as in the biorhythms and the functioning of the brain and the normal spriinyatt.

You can remember the golden proportions, just as respectfully marvel at the bird's egg.

If we marvel at the beautiful countryside, we are stunned by everything. Let's pay attention to details. Richtsі, what to play for a great tree. Bachimo field is green. Let's remember, as the wind hits him low and the scolding hits the grass from the side. We can smell the aroma of nature and feel the spiv of birds ... Everything is in harmony, everything is mutually sympathetic and gives a touch of peace, beauty. Where do you sit on the lava: on the edge, in the middle, or in some place? Greater vіdpovіst, scho trochs gave in the middle. Approximate size of the proportion of lava in your body to the edge will be 1.62. So in the cinema, in the library - skrіz. Instinctively we create beauty in harmony, as in the whole world I call it "Golden Peretina".

Mathematics has a golden edge

Have you thought about how you can signify the beauty of the world? It appears, from a mathematical point of view it is possible. Simple arithmetic gives an understanding of the absolute harmony, as it appears in the hopeless beauty of the weeds to the principle of the Golden feather. Architectural disputes In Egypt and Babylon, they were the first to follow this principle. Ale formulating the principle by the first Pythagoras. In mathematicians, the score was three times more than half, or rather 1.628. Does spіvvіdnoshennia seem like? \u003d 0.618 \u003d 5/8. A small double = 0.382 = 3/8, and a larger double is taken as one.

A:B=B:C and C:B=B:A

According to the principle of the golden linen, great writers, architects, sculptors, musicians, - people of mysticism, and Christians, who paint with pictograms (five stars, etc.) with yoga elements in temples, roaring in the presence of evil spirits, and people, yak exact sciences, the virishal problem of cybernetics.

Golden pererіz in nature and manifestations.

Everything on earth is in full shape, growing uphill, killing or spiraling. Archimedes respectfully added respect to the rest, making equal. According to the Fibonacci series, a cone, a turtle, a pineapple, a dormouse, a hurricane, a cobweb, a DNA molecule, an egg, a grandmother, a lizard are crowned.

Tіtsіrius dovіv, that our entire Vsesvit, space, galactic expanse - everything is planned out of the Golden principle. Absolutely for every living thing, that not alive one can read the greatest beauty.

The golden veil of a human.

The brushes are thought out by nature and are designed with a proportion of 5/8. I don't include people's warnings about "broad brushes". Most of the parts of the body in spivvіdshennyah zastosovuyutsya until rivnyannia. As all the parts of the body are rooted in the Golden Formula, then the same given data will be more suitable and ideally folded.

Ridge from the shoulders to the top of the head and її razmіru = 1:1.618
Vіdіzok vіd navel to the top of the head and vіd shoulders to the top of the head = 1:1.618
Vіdrіzok vіd navel to kolіn i vіd them to stupn_v nіg = 1:1.618
Vіdіzok vіd pіdborіddya to the extreme point of the upper lip and її to the nose \u003d 1: 1.618

mustache in the case of individuals to give a wild statement about the ideal proportions, what to look at.
Fingers, palms, tezh podkoryayutsya law. It is also necessary to indicate that the hands are spread out with the tulub of a healthy growth of people. That there, all organs, blood, molecules follow the Golden Formula. Right harmony in the middle of that call of our expanse.

Parameters from the physical side of the most important factors.

Thickness to sound. The main point of the sound, which calls out is not comfortable, but the sound at the ear shell = 130 decibels. This number can be divided by the proportion of 1618, then go out, the sound of a human cry will be = 80 decibels.
In the same way, rushing far away takes 50 decibels, which is typical for the normal thickness of a human being. І the remaining sound, which is taken away from the beginning of the formula, is the receiving sound of a whisper = 2.618.
Following this principle, you can choose the optimally comfortable, minimum and maximum number of temperature, pressure, moisture. The simple arithmetic of harmony is embedded in our most refined.

Golden veneer at the mystic.

In architecture, there are many things to consider: the Egyptian pyramids, the Mayan pyramids in Mexico, Notre Dame de Paris, the Greek Parthenon, the Petrovsky Palace and others.

At the music: Arensky, Beethoven, Havan, Mozart, Chopin, Schubert and others.

In painting: mayzhe OAO All the paintings of famous hudozhnikіv napisanі zgіdno of pererіzom: rіznostoronnіy Leonardo da Vіnchі i reentrant Mіkelandzhelo, takі rіdnі in pisannі Shishkіn of Surіkovim, іdeal naychistіshogo Mistetstvo - іspanets Rafael, i іdeal zhіnochoї beautiful - іtalієts Bottіchellі, i hto bagato.

In poetry: the language of Oleksandr Sergiyovich Pushkin, especially “Evgeny Onygin” and the verse “Shvets”, the poetry of the miracles of Shota Rustaveli and Lermontov, those other great masters of the word, are sorted.

At the sculpture: a statue of Apollo Belvedere, Zeus of Olympia, beautiful Athena and graceful Nefertitis, and other sculptures and statues.

Photography wins the "rule of the third". The principle is this: the composition is divided into 3 equal parts vertically and horizontally, the key moments are spread either on the lines of the peretina (horizon) or at the points of the peretina (object). In this order, the proportions are equal 3/8 and 5/8.
Vіdpovіdno to the Golden Pererazu є rich cunning, like varto sorted out in detail. I will describe them in a report to the offensive.

Uchni 9 "A" class

We are unequally placed before the subjects and the manifestations of the necessary activity. Effortlessness, formlessness, restlessness are accepted by us as more indulgently and to cope with hostility. And the objects of that manifestation, like the dominion of the world, dotality, that harmony, like a garnet, call out to us, a little suffocated, joy, raise mood. People from long ago were praised by food, which are in such incomprehensible speech as beauty and harmony, be like mathematical roses. The Danish project of assignments to one of such mathematical relationships, there, de vono, one can see the harmony of that beauty.

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The essence of that zastosuvannya golden peretina in the life of people

Relevance to those Yak the role of the golden tulle in the life of a person? We are unequally placed before the subjects and the manifestations of the necessary activity. Effortlessness, formlessness, restlessness are accepted by us as more indulgently and to cope with hostility. And the objects of that manifestation, like the dominion of the world, dotality, that harmony, like a garnet, call out to us, a little suffocated, joy, raise mood. People from long ago were praised by food, which are in such incomprehensible speech as beauty and harmony, be like mathematical roses. The Danish project of assignments to one of such mathematical relationships, there, de vono, one can see the harmony of that beauty.

Nutritional problems Does life have a golden veil? In which areas do golden veils stagnate?

Meta: 1. Broaden the horizons of learning, take on the development of educational interest. 2. Show schoolchildren the deep intellectual meaning of mathematics. 3. Adopt the knowledge of the laws of beauty and harmony of the present world.

1. Vivchiti geometric design of the "golden cut"; 2. Increase the power of the algebra of golden proportions; 3. Find out about zastosuvannya golden peretina in mathematics; 4. Vivchiti zastosuvannya golden peretina at life; 5. Adopt the knowledge of the laws of beauty and harmony of the present world; 6. Show schoolchildren the deep intellectual meaning of mathematics. manager

Methods 1. Collection of information 2. Questionnaire for students 3. Work with different dzherels 4. Robot with a computer

Follow-up plan 1. The concept of “Golden cut” 2. Historical proof 3. Geometrical reasoning of the “golden cut” 4. Concept of the Golden tricot 5. Concept of the Golden rectangle 6. Concept of the Golden spiral 7. Proper pen of the pen 8. Symbol “9. "Golden Peretin" in: - nature - art - architecture

Head of work on the project Organizational moment 2. Designated task 3. Drawing up a hypothesis 4. Devided into groups 5. Selection of theoretical material 6. Questionnaire 7. Analysis and processing of information 8. Demonstration of the project

Feedback: Do you know V about the “Golden Pereteen”? Would you like to know more about "Zotol Peretina"? Do you want to know about the "Golden peretin"?

Geometry of Volodymyr has two treasures: one of them is the Pythagorean theorem, and the other one is subdivided into the middle one and the last one. I. Kepler

What is the golden peratin?

h: b \u003d b: a a: b \u003d b: c Golden pereraz - tse such a proportional rose under the vіrіzka on the nerіvnі parts, while the entire vіrіzok is so brought up to the largest part, like the largest part is brought down to the smallest; or, in other words, the smaller one is so brought up to the bigger one, like the bigger one to the whole.

With a golden cut, the crown of the larger crown is the middle proportion of the crown of the entire crown and the smallest part.

numerical meaning of the "golden promise"

The pentagram to post is adorned with the diagonals of the correct p'yatikutnik, tobto. correct p'yatikutna zirka. The diagonals of the correct p'yatikutnik are divided by the point of the "golden proportions" line, that is. vikonuetsya already known to us jealousy:

Golden tricoutniks Leather with a p'yatikutny zirka є with a golden tricoutnik. The dominance of the kut at the top of the road 36; base, added to b_k divide її in the proportion of "golden cut"   АС: С D = CD: AD CD = BC

Fibonacci numbers In golden proportion, closely interlocking a series of Fibonacci numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc. on the third, the sum of the two in front "Kepler: "... the order of numbers to stand between pragne to the golden proportion of Fibonacci.

The main proportions in the human figure and appearance

the height of the guise (up to the root of the hair) is carried to the vertical stand between the arches of the brows and the lower part of the chin, as if it were between the lower part of the nose and the lower part of the chin

The golden proportion was won by ancient sculptors. In the house of gold, the proportion of the statue of Apollo Belvedere: the growth of the depicted person is divided by the umbilical line at the golden perimeter.

Apollo Belvedere

Zeus Athena Olympian Parthenos

Vymіryuvannya k_lkoh tysyach human tіl allowed to reveal: - for non-mothering tse vіdshennya dоrіvnyuє - 1/1 for grown-up people - 13/8 = 1.625 for grown-up women - 8/5 = 1.6 .

"Golden peretin" in painting

One of the most popular works art - a portrait of Moni Lizi (La Giocondi) for many years attached the respect of the elders, as they showed that the composition of the little one is based on golden tricots, which are parts of the correct pyatikutnik.

Portrait of Monnie Lizi (La Giocondi) dovgі roki attached the respect of the elders, as they showed that the composition of the little one is based on golden trikutniks, that it is parts of the correct pyatikutnik.

Having finished the fairy tale, Leonardo looked at Monna Lisa, and his face shone with light, his eyes shone. Then, slumped over like a dream, she sighed, passed her hand in disguise, and without a word went to her place, folded her hands and assumed a splendid pose. Ale on the right is bula zroblena - the artist awakened the baiduzha statue; a smile of bliss, quite familiar with її disguise, was lost in the cloaks of the company and tremtіla, giving the guise of a marvelous, enigmatic and trohi sly viraz, like a person, like a cognizance of a mystery, Leonardo movchki pratsyuvav, afraid to miss this moment, this promin sun, scho illuminating this boring model.

Shishkin - " Sosnovy Guy On this famous painting I. I. Shishkin, the motifs of the golden peretina are clearly visible.

Back in the Age of Resurrection, artists realized that whether a painting could have singing points, like a momentary riveting of our respect, this is the name of the golden center. It doesn't matter at all what format the picture can be - horizontal or vertical. Such dots of the entire chori, they add the size of the image horizontally and vertically to the golden perimeter, tobto. roztashovani stench on vіdstanі approximately 3/8 and 5/8 vіd vіdpovidnih edges of the plane.

"Golden Peretin" in architecture

"Architecture - the most important thing is three things: beauty, tranquility and spirituality of life ... Until what reach can serve as a key to knowing proportions, perspective, mechanics, or physics, and to all the sleepy leader is reason." V. Bazhenov

One of the most beautiful works of ancient Greek architecture is the Parthenon (V century BC)

You can see it on the little ones whole row patterns tied with golden feathering. The proportions of the future can be shown through different steps of the number Ф = 0.618 ... On the plan of the Parthenon, one can mention the “golden rectangles”.

Pantheon

We can also sing gold in the wake of the Cathedral of Our Lady of Paris (Notre-Dame de Paris):

Architekturni budіvlі vykonanі on the basis of "golden peretina"

Budinok Pashkov in Moscow

Algebra of music Music is the magic of sound, ... sound is the very matter of music ... sound can be quiet, sound can rest in silence, like expensive stone in oxamite screen. Heinrich Neuhaus

The largest number of musical creations that create a "golden feather" is among the brilliant authors Haydn (97%), Arensky (95%), Scriabin (90%), Chopin (92%). Beethoven (97%) Mozart (91%) Schubert (91%)

In 1770 creations of 42 composers, 3275 golden revisions were made. In 27 sketches by Chopin, 154 golden borders were revealed;

Mathematics of verses In the future rich artistic creations, gold proportions and Fibonacci numbers are manifested. A.S. Pushkin. born 1829-1836 109 lines - 4 to 116 rows. The middle rozmіr tsikh vіrshiv becoming 88 rows. The tops See the largest expansions - 5,8,13,21,34 - close to the number of the Fibonacci series

V.Ya. Bryusov. 18 82 -1 912 rubles 360 lines of creations in 8 - 36 rows. The middle rozmіr tsikh vіrshiv becoming 18 rows. The largest widths are seen - 8,13,21,34 - close to the number of the Fibonacci series

Prose by A.S. Pushkin. "Pikova dama" 6 rows 853 rows. Culmination - 535th row  853:535 = 1.6 1 split 110 rows. Culmination - 68th row  110:68 \u003d 1.62 2 split 219 rows. Culmination - 135th row  219:135 \u003d 1.62 3 split 212 rows. Culmination - 131st row  212:131 \u003d 1.62 4 split 113 rows. Culmination - 70th row  113:70 \u003d 1.614 5 split 75 rows. Culmination - 46th row  75:46 \u003d 1.63 6 divided 124 rows. Culmination - 77th row  124:77 \u003d 1.62 Golden proportion - the whole harmony. In such a manner, A.S. Pushkin felt like harmony was superbly blamed, which confirms the genius of the great poet and writer

Geometry of Volodya has two treasures: one of them is the same Pythagorean theorem, and the other one is split into the extreme and the middle one. First you can equalize from the world of gold; to another, I guess an expensive stone. Johannes Kepler

Visnovok Mi was stitched and patted that the “golden tulle” is widely stagnant in the rich cloakrooms of science. That's why it's "gold".

The golden cut is a universal manifestation of structural harmony.

It thrives in nature, science, mysticism - in everything, with which a person can shut up. As if having known the golden rule, the people did not change it anymore.

The designation of the golden webbing

The most important thing for me to note is that a smaller part is brought up to a larger one to the whole. An approximate yogo value is 1.6180339887. In a rounded height value, the proportions of the parts of the whole are balanced as 62% by 38%. Tse spіvvіdnoshnennia di forms of space and hour.

The old-timers dipped in a golden peratin in the image of the cosmic order, and Johann Kepler called yoga one of the treasures of geometry. Today's science sees the golden thread as "asymmetric symmetry", calling it a universal rule in a broad sense, which reflects the structure and order of our light arrangement.

The history of the golden recut

The ancient Egyptians were aware of the golden proportions, they knew about them in Russia, and even before that, the black Luca Paccioli explained the golden proportions scientifically in the book “Divine Proportion” (1509), illustrating to that, ymovirno, by Leonardo da Vinci. Pacholi vbachav the divine trinity at the golden perimeter: the small vіdrіzok escorted Sin, the great one - the Old Man, and the whole - the Holy Spirit.

Without a middle rank, according to the rule of the golden cross, the name of the Italian mathematician Leonardo Fibonacci was tied. As a result, the variance of one of the tasks of the teachings of viishov on the sequence of numbers, at the same time as a series of Fibonacci: 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on. Kepler turned his attention to the ratio of succession to the golden proportion: to the point of indiscretion". Nini series of Fibonacci is the arithmetic basis for the proportions of the golden line in all yogo manifestations.

Leonardo da Vinci also consecrated to a rich hour the embedding of the features of the golden peretina, so that the term itself can be laid down for everything. Yogo little ones of a stereometric body, adorned with the correct p'yatikutniks, bring that the skin from the otrimanih with the retiring of the straight cuts gives spivvіdshennja sides at the golden rose.

Over the years, the rule of the golden peretina has been transformed into an academic routine, and in 1855 the philosopher Adolf Zeising turned his life to a friend. Vіn dovіv to the absolute proportion of the golden peretina, robyvshi їх universal to all manifestations of the world. Vtіm, yogo "mathematical nature" called out a lot of criticism.

The Golden Crossing of Nature

Navit not vdayuchis at the rosewood, a golden pereriz can easily be seen in nature. So, under the new one, we use the tail and body of the lizard, between the leaves on the head, and the golden edge and at the shape of the egg, as if to draw a smart line through the widest part of the yogo.

The Belarusian scholar Eduard Soroko, who has twisted the forms of golden undergrowth in nature, declaring that everything that grows and is able to take its place in space, is endowed with the proportions of a golden peretina. On the other hand, one of the most famous forms is twisting in a spiral.

More Archimedes, adding respect to the spiral, viviv on the basis of the form of equalization, like and at once zastosovuetsya at the technical. Pіznіshe Goethe, denoting the gravity of nature to spiral forms, calling the spiral “life crooked”. By the present time it has been established that such a manifestation of spiral forms in nature is like a shell of a ravlik, a rosemary of a dormouse plant, a pavutin's head, a hurricane's ruin, a DNA of Budova and to inspire the structure of galaxies to avenge the Fibonacci series.

Golden peretin that people

Models and designers wear all rozrahunka to shy, out of the proportions of the golden peretina. Lyudina is a universal form of revising the laws of the golden peretina. Obviously, in nature, far from all people have proportions that are ideal, which create songs of folding with the choice of clothes.

The child of Leonardo da Vinci has little ones inscribed in the colo of a naked person, who are trying on two overlays one on one position. Spiryuchis on the achievements of the Roman architect Vitruvius, Leonardo tried to establish the proportions of the human body. The late French architect Le Corbusier, victorious "Vitruvian people" by Leonardo, having created a natural scale of "harmonious proportions", which blew into the aesthetics of architecture of the 20th century.

Adolf Zeising, maintaining the proportion of a human being, having achieved a colossal work. Vіn miryav close to two thousand human bodies, as well as impersonal ancient statues and vivivs, that a golden cut is vyslovlyuє average statistical law. In humans, it is possible to order all parts of the body, and the head of the head of the golden cut of the head pierced the body with the point of the navel.

As a result, the last one was vindicated, having established that the proportions of the human body 13:8 are closer to the golden feathering, the lower proportions of the female body are 8:5.

The art of spacious forms

The artist Vasil Surikov said, “that the composition has a non-transverse law, if in the picture it is impossible not to tidy up, add, put an end to it, it’s impossible to put an end to it, mathematics is right.” For a long time, the artists were intuiting this law intuitively, but after Leonardo da Vinci, the process of creating a painting canvas could not do without the completion of geometrical tasks. For example, Albrecht Dürer for the designation of the points of the golden cut of the vicorist, having found the proportional compasses.

Historian F. V. Kovalyov, having reportedly finished the painting by Mikoli Ge “Oleksandr Sergiyovich Pushkin near the village of Mikhailovskiy,” he indicates that the leather detail of the canvas, the fireplace, the bookcase, the armchair sings itself, beautifully inscribed in golden proportions.

The successors of the golden peretina unobtrusively twist and freeze the masterpieces of architecture, stverzhuyuchy, stench became such, to the creation behind the golden canons: the Great Pyramid of Gizi, the Cathedral of Our Lady of Paris, the Cathedral of St. Basil the Blessed, the Parthenon.

And now, in whatever mysticism of spacious forms, the proportions of the golden peretina, shards of stink, on the thought of the mysticists, make it easier to take on the creation, are shaped by the gazer more aesthetically.

Word, sound and movie

Form the Timchas art in your own way to demonstrate the principle of the golden hem. Literary scholars, for example, brought back respect, that the most popular number of rows at the top of the last period of Pushkin's work corresponded to the Fibonacci series - 5, 8, 13, 21, 34.

Dіє the rule of the golden peretina th in the well-taken creations of the Russian classic. So the climax of the "Dame of Spades" is the dramatic scene of Herman and the countess, who will end with the death of the rest. The line has 853 rows, and the climax sits on the 535th row (853:535 = 1.6) - the point of the golden crossbar.

Radyansky music scholar Ege. K. Rozenov demonstrates the exactness of the golden feathering in strict and free forms of Johann Sebastian Bach's creations, which reflects the thoughtful, watchful, technically vibrated style of the master. It is fair and worthy of the most famous works of other composers, dey fall on the point of the golden peretina the most beautiful chi of the unsound musical solution.

Film director Sergiy Eizenstein wrote the script for his film “Battleship Potiomkin” according to the rule of the golden line, dividing the line into five parts. At the first three branches, the ship is roared by the ship, and the remaining two are in Odessa. Transition to the stage near the city and gold is the middle of the film.

Look back: 1,557

Yakovlev Olena

Meta roboti - to understand the Golden Perez, take a look, like the Golden Pereriz is beaten by nature.

In the abstract, the concepts of the Golden Perecution, the Golden Rectangular, the Golden Spiral and yoga stasis in nature are clearly seen. Described doslіdzhennya, carried out at the class.

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Front view:

Municipal mortgage

"Secondary education school No. 48"

MISKA SCIENTIFIC AND PRACTICAL CONFERENCE

Section: mathematics, biology

"Golden veneer in nature".

MOU m. Kurgan "ZOSH No. 48",

8 "B" class.

Science books: Yakushchenko

Tetyana Oleksandrivna

teacher of biology,

MOU m. Kurgan "ZOSH No. 48",

Baeva Liliya Mykolaivna,

MOU m. Kurgan "ZOSH No. 48",

Mathematic teacher.

Mound,

2010

Side entry
Understanding the golden cross section of side 5
History of the Golden section of the side.
Golden rectangle side 7
Gold spiral
Golden spirals in living nature side 9
The most important phyllotaxis page 10
Golden cross at nature side 11
Golden proportions for the people on the side.12
My next page 13
Visnovok side 13
Addendum stor.
References page 15

Intro. About living that non-living nature.

Nature, sprynnyat as a veil of light in various forms, is composed of two parts: living and inanimate nature. Why is there a difference between them?The creations of inanimate nature are characterized by a high stability, a weak sluggishness, as judged in scale human life. The people are growing, alive, old, dying, and the granite burns (adj. 1) are overgrown with the same and the planets turn around the Sun just like that for Pythagoras's hour.

The world of living nature stands before us as something else - crumbling, timid and completely different. Life is showing us a fantastic carnival of diversity and originality of creative combinations! (Supplement 2)The world of inanimate nature is the light of symmetry that gives us the stability of that beauty. The world of living nature - tse usampered the world of harmony, at the yakіy deіє the law of the Golden cross.

Tsіl my robots - to understand the Golden Peretina, take a look, like the Golden Pereraz vikoristovuetsya nature.

3 meti squeal task:

Vivchiti literature on this topic;

Vivchiti understand the "Golden peretin", look at how the "Golden peretin" is victorious by nature;

Dzherelami doslіdzhennya z'appeared:

library fundi;
Internet;
library of my scientific ceramics.

follow-up methods:

collection of materials on the topic;
work from the class;

Understanding the Golden Reverse

Golden edge (gold proportion, podіl at the extreme and the middle ratio, harmony podіl, φ) - podіl prіzka on the part in such a spivvіdnoshennі, with a smaller part, it goes up to the big one, how big it is to the whole as a whole. For example, I split the section of AC into two parts in such a way that the greater part of AB is brought to the smaller BC so that the entire section of AC is brought to AB (that is | AB | / | BC | = | AC | / | AB |). (add.3) It is accepted to designate the proportion as a Greek letter, φ і won’t be more expensive: 1.618 (add.4)

The thirds of the golden proportion are expressed by the irrational infinity fraction 0.618... so to take c for unity, a = 0.382. The numbers 0.618 and 0.382 are Fibonacci sequence coefficients. On this proportion, the main geometric positions are based.

If you go to an empty bench and sit on it, then you won’t sit in the middle of the lava (as immodestly, wanting to chirp and have such a clearly pronounced character) and, obviously, not on the edge. If you indefinitely freeze the house, if you divided the bench on your body, then you will see that the increase in the large air intake to the smaller air intake is approximately 1.62. The whole number, called the Golden Peretina, is included up to the trio of the most important irrational numbers, that is, such numbers, dozens of such numbers, which are unrestricted and non-periodic.

History of the Golden Peretina.

It is accepted to understand that Pythagoras, an ancient Greek philosopher and mathematician (VI century BC), understood about the Golden Age of centuries. Є pripuschennya, that Pіthagoras his knowledge of the golden podіlu zapoziv among the Egyptians and the Babylonians. The Greeks were right geometers. Learn arithmetic taught their children for help geometric shapes. The square of Pythagoras and the diagonal of the square were the basis for stimulating dynamic rectangles.
Plato (addition 5) (427...347 BC) also knew about the golden podіl. Yogo dialogue "Timei" of assignments to the mathematical and aesthetic views of the school of Pythagoras I, zokrem, nourishment of the golden hem. At the facade of the ancient Greek temple of the Parthenon there are golden proportions. In ancient literature, which has come down to us, the golden hem is first guessed in Euclid's "Cobs" (Appendix 6). After Euclid, the golden rose was occupied by Gipsikl (II century BC), Pappus (III century AD) and in. Translating J. Campano from Navarri (III century) zrobiv for translating comments. The secrets of the golden podіlu were jealously guarded, saved from the secret crypt. The stench of the bouli vіdomі is less sacred.
In the epoch of Renaissance, there is an interest in the golden hem of the middle classes and artists in connection with yoga zastosuvannyam like geometry, as well as in art, especially in architecture.
Luca Pacioli (app. 7) miraculously understood the meaning of the science of art. In 1496, at the request of the Duke of Moreau, he came to Milan to read lectures on mathematics. At Milan, at the court, Moro was also the father of Leonardo da Vinci (Appendix 8). In 1509 p. near Venice, a book by Luca Pacioli "Divine Proportion" was seen with brilliantly illustrated illustrations, through which you can appreciate that Leonardo da Vinci created them. The book was swamped by the anthem of the Golden Proportions. In the midst of the richness of the golden proportions, the monk Luca Pacioli did not fail to name and її the “divine essence” as a manifestation of the divine trinity god sin, god father and god the spirit of saints

golden square

The golden edge is already widely celebrated in geometry. Let us commend our dear geometrical powers of the Golden Perecution from the Golden Rectangular, as it may be more geometrically appointed. A golden rectangle is such a rectangle, which has a larger side to a smaller equal golden proportion (app. 9) We can look at the simplest Golden rectangle, if AB \u003d and BC \u003d 1. (app. 10)

The golden rectangle has a lot of unimaginable powers. Vіdrіzavshi vіd golden pryamokutnik square, the side of which is the smaller side of the pryamіrіv, we again take away the Golden rectangle of smaller sizes. Selling squares, we will take smaller and smaller Golden rectangles. Moreover, the stench will be sorted along a logarithmic spiral (Appendix 11), what can important meaning in mathematical models of natural objects (for example, shells of rabbits). The pole of the helix lies on the bridle of the diagonals of the cob bud BD and the first vertical one, which crosses AC. Moreover, the diagonals of all the advancing Golden rectangles, which change, lie on these diagonals (Appendix 12)

Golden peretin bov v_domy ancient Greeks. One can hardly doubt that the ancient Greek architects and sculptors celebrated yoga in their creations. The butt can buti want to use the Parthenon. The American mathematician Mark Barr, when he called out the name of the two windings that make up the golden peretin, is the very thing and mathematician. Letter (fi) - the first letter of the name of the great Phidias.

In that hour, like the Golden Peretina and the Golden Rectangular, they represent static forms of natural and created by human beauty and activity, manifested aesthetically attached to dynamism, organized growth and development can be vykonan but the most beautiful form of the All-Sveta - the Golden Spiral.

Gold spiral

A golden rectangle can be twisted to induce a golden spiral. Whether a Golden rectangle can be divided into a square and a smaller Golden rectangle. This process can theoretically be continued to infinity. Qi rectangles, like mi painted and like, like it appeared, twisted in the middle, marked A, B, C, D, E, F and G (Appendix 13) the diagonals and exactly indicate the theoretical center that the squares twist. Approximately from the central point, we can cross the spiral (app. 14), by connecting the points to the peretina of the skin square, which twists, in the order of growth of the world. So, as the squares are twisted in the middle of that name, their points of confluence are inscribed to the Golden Spiral. To inspire the Golden Spiral, the same process can be carried out, as well as for the twisted twists.

At any point, the development of the Golden Spiral, extending the length of the arc to її diameter is more than 1.618. Diameter and radius in their line are combined with diameter and radius, which are at a distance of 90 degrees, with a coefficient of 1.618 (app. 15), Gold spiral, as well as a variety of logarithmic and non-wignan spirals

fast form. From whether or not the points of the spiral can collapse indefinitely, or directly in the middle, or the names. The central part of the logarithmic spiral, looked at through a microscope, is small for the very widest part that is visible on the far-flung rich light rocks.

Golden spirals in living nature

Golden spirals are widely widened in the biological world. As it was conceived more, the horns of creatures grow in less than one stroke. The growth rate works on a logarithmic spiral. At the book "Crooked Lines in Life" by T. Cook see different spirals that appear at the horns (app.16) of rams, kiz, antelopes and other horned creatures. Among the impersonal spirals of the wines, choose the Gold spiral (the curve of the harmonic growth) that looks like a symbol of evolution and growth.

Spirals widely manifest themselves in living nature. Ruslin whiskers spirally twist (Appendix 17), fabrics grow in a spiral at the stovburs of trees, in a spiral, weave in a dormouse, spiral ruhi (nutations) are guarded when the roots of those pagons grow. Obviously, in whom there is a decline in the organization of growing, and її the root trace of shukat on the clitin and molecular level.

A spiral-like shape is made by more shells (dod.18-19). Vivchayuchi designs of shells, vcheni raised respect dotsіlnіst forms and the surface of the shells: the inner surface is smooth, the outer surface is corrugated. In the middle lies the body of a mollusk - the inner surface can be smooth. Older ribs increase the hardness of the shell and in such a way promote the її mіtsnіst. The shape of the shells opposes its thoroughness and the economy of koshtiv, stained glass on the її creation. The idea of the spiral in the shells is not expressed close, but in a thorough geometrical form, in a completely beautiful, “detailed” design.

Russian opinion S.V. Piven, showing the schemes of the life of the musculoskeletal apparatus in various vertebral creatures, told a story about those that the development of their kintsivok was due to the influx of two factors: the laws of the Golden Proportion and the attachment of the body to the way of life:

"The laws of the Golden Proportions marked out the main plan, the main idea of the design of the kіntsіvok, and the specific minds of the skin creatures zoomed in on inspiration - fluctuations in accordance with this plan, all the differences of life and the essential forms."

The most impressive phyllotaxis.

Characteristic rice budovi roslin and їх development є

helicity. Sche Goethe, what a bov not only a great poet, but th

nature-probing, respecting the spiralness of one of the characteristic signs of all organisms, manifesting the most significant essence of life. The whiskers of the roslin are spirally twisted, the growth of fabrics in the stovburs of trees is growing in a spiral, the weaving in the dormouse is growing in a spiral, the spiral ruhi (nutacia) is guarded by the growth of the roots of those pagons. Obviously, in whom the decline in the organization of growths is manifested, and її the root trace of shukat on the clitin and molecular levels.

There are no sumnivivs, that the recessionary spiral is one of

The main power of the organisms is one of the most important signs of the living. At a glance, it seems that the crystals of inorganic speeches have a helicity and a twisted structure. However, more profound studies have shown that the twisted dislocation of atoms is also observed in some crystals and manifests itself in the concept of twisted dislocations. Such crystals are formed from a single screw-like curved atomic plane. In case of skin circulation, the area rises about the axis

for one crochet of gvint, which is more expensive in the middle of the city. It should be added that crystals with such a twint structure can be arrogant. In the twisted structure of DNA molecules to the twisting of the roslins - such forms show the helicity of the different levels of the organization of the roslins.

The peculiarity of the organization of roslin is clearly manifested in

regularities of leaf tasting.

Іsnuє kіlka ways of leaf threshing. At the first leaf

vtechі roztashovuyutsya strictly one pіd one, utvoryuyuchi vertical rows - orthostіhi. A smart spiral, which is the last month of leaf growth on the branches, is called a genetic, or the main spiral, more precisely, a screw line and subdivided into a number of leaf cycles. This gwent is called genetic by shards of rotting of leaves in a new order, appearing in a new leaf. The projection on the plane of the leaf growth allows in parts of the cola to sprout the leaves.

I looked at the regularity of the rotting of leaves, little grass, nasinnya

called phyllotaxis. It is installed that when rotting

leafing under an ideal hood, the leaf will not be rotting exactly above the other, below it will be created best mind for photosynthesis

Golden feather in nature.

Everything that swelled like a form, settled down, grew up, jumped to take a place in the open space and save it for itself. It is important to know the development mainly in two options - growing uphill or spreading on the surface of the earth and twisting in a spiral.

Roslin - chicory (adj. 20) is unremarkable among roadside grasses. Let's be respectful. Vіd the main stalk utvilis vіdrostok. Immediately, the first leaf was rotting. The second is to break a strong wikid in the open, zupinyaetsya, let out a leaf, but it is shorter than the first one, again to break the wikid in the open, but even less strength, let out a leaf of an even smaller size and renew the wikid. If the first wikid is taken as 100 ones, the other one is equal to 62 ones, the third - 38, the fourth - 24 and so on. Dovzhina pelyustok tezh under the order of the Golden Proportions. In the growing country, conquered by the expanse, the growth took the same proportions. The impulses of this growth step by step changed at the proportion of the Golden cross.

The lizards at first glance catch the proportions for the eye - the length of the tail so lie down to the length of the body, like 62 to 38 (Appendix 21).

Golden proportions for this people.

At 1855 p. German researcher of the Golden Peretina, Professor Zeising, published his work "Aesthetic Research". With Zeising, it became the very one who is a little inevitable to become a successor, who looks at the manifestation as such, without a link with other manifestations. Vіn absolutizing the proportion of the Golden peretina, voicing її the universal manifestation of nature and mysticism.

Zeising and his numerous successors, ale buli and opponents, as if they voiced his opinion about the proportions of "mathematical aesthetics".

Zeising Vikon in a colossal robot. Winning close to two thousand human bodies and deyshov vysnovka, that the Golden peretin bends the average statistical law. Podіla tіla point to the navel - the most important indicator Golden crossover. The proportions of the human body are fluctuating in the middle of the average ratio 13: 8 = 1.625 and sometimes come closer to the Golden Peretina, the lower proportions of the female body, where a similar average proportion is observed in the average ratio 8: 5 = 1.6. At the new people, the proportion should be 1: 1, up to 13 years old it will be 1.6, and up to 21 years old people. The proportions of the Golden Perecution are shown also in other parts of the body - the shoulder dorsum, the front of the hand and the hand, the hand and fingers thin. (Appendix 22).

My follow up.

I looked at the rooms in the school and at home and saw those that grow behind the laws of the Golden Peretina (Appendixes 23 - 29) and those that grow behind the laws of the Golden Spiral (Appendixes 30 - 34).

At the class, I spent the next step - I shouted to the lads to sit on the lava. All data are included in the table (Appendix 35), a rotting of water was carried out to the greater part and the greater part to the lesser part. Viishlo approximately 1.6. Tse i є Golden peretin.

Visnovok.

People are divided into different objects by shape. An interest in the form of any object is that it is possible to dictate life's needs, and it is possible to call out the beauty of the form. The form, which is based on being based on the symmetry of the Golden Perecution, spriya to the best starry sprinyattyu that appearance of beautiful beauty and harmony. The whole is always added up from parts, parts of different sizes are changed from one to one to the whole. The principle of the Golden Fringe is the greatest manifestation of the structural and functional perfection of the whole and yogo parts in the art, science, technology of nature.

List of references

M. Vasyutinskiy "Golden Proportion" - M., "Young Guard", 1990
A. Azevich "Twenty Lessons in Harmony" -M., "School-Press", 1998
M. Gardner "Mathematical puzzles and roses" -M., "Svit", 1971
D. Pidou "Geometry and Art" - M., "Svit", 1989
Encyclopedic Dictionary of a Young Mathematician - M., 1989
Magazine "Quantum", 1973 No. 8
Journal “Mathematics in school”, 1994, No. 2, No. 3