Where do isosceles triangles meet in real life? Educational project "Triangles in our life

Using Triangles in Practice

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Triangles are our world Prepared by Kuznetsova Natella Student of the 7th "A" class Teacher: Polina Vasilievna Malyukina MOU "Gymnasium with. Ivanteevka, Ivanteevsky district, Saratov region

If you look around you, you can conclude that we are surrounded by triangles everywhere. Here are some simple examples.

And so, in our house we can see pillows, tables, different shelves, lamps, and even erasers shaped like a triangle.

Also, there are many triangular-shaped pastries.

Another good example- tent or hut.

In Paris, they invented the "technology for the construction of triangular houses."

There are special markings near bus stops.

The mountains also have the shape of a triangle.

Pyramids of Egypt.

Conclusion Triangles are found everywhere. The circle and the triangle are the two fundamental figures. For example, a square may consist of two, three, four triangles.

Thank you for your attention!

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Triangles Completed by: Basova Lera

Consider the various dwellings of people: wigwam, yurt, tent. All of them have a conical shape, a triangle is obtained in cross section. Such structures are easily blown by the winds, water quickly drains from them. The roofs of old wooden houses and modern high-rise buildings are triangular in shape. This is due to the fact that melted snow does not linger on such roofs and rainwater easily drains. Triangular roof of the house: http://festival.1september.ru/articles/505238/

Now we send letters in rectangular envelopes, but earlier, during the war, letters had a triangular shape. Soldier's triangle - a letter without a stamp and an envelope, sent by a soldier from the front or a soldier to the front. http://festival.1september.ru/articles/505238/

Consider the pyramids. We saw that side faces of these pyramids have the shape of a triangle, all side faces are equal. AT Ancient Egypt The pyramids served as the tombs of the Egyptian pharaohs. The largest of them - the pyramids of Cheops, Khafre and Menkaure - in ancient times were considered one of the seven wonders of the world. The pyramids were given special, cult honors, since their construction was supposed to express the mystical identity of the country and its ruler. We all strive for excellence. The energy of the Earth, passing through the wide base of the pyramid, tends upward into space. The buildings in El Giza, with their grandeur and apparent uselessness, amazed the imagination already in antiquity, which is best conveyed by the Arabic proverb: "Everything in the world is afraid of time, but time is afraid of the pyramids." Pyramids of Egypt. http://festival.1september.ru/articles/505238/

http://en.wikipedia.org/wiki/ Triangle

Triangle (lat. Triangulum, Tri) is a constellation in the northern hemisphere of the sky. Occupies an area of ​​131.8 square degrees in the sky, contains 25 stars visible naked eye. In the Triangle is spiral galaxy M33 (the Triangulum galaxy), the third largest in the Local Group. The stars of the Triangle are not bright: α is only the third magnitude. In total, 15 stars can be counted in the constellation. Through a telescope, you can see double starι, the components of which are colored in golden yellow and green-blue. http://en.wikipedia.org/wiki/ Triangle_ (constellation)

http://images.yandex.ru/yandsearch?text=%D0%BD%D0%BE%D0%B2%D1%8B%D0%B9%20%D0%B3%D0%BE%D0%B4%20 %D0%BA%D0%B0%D1%80%D1%82%D0%B8%D0%BD%D0%BA%D0%B8&stype=image&noreask=1&lr=194 Also, the Christmas tree has a triangular shape

There are also Triangular curtains http://images.yandex.ru/yandsearch?text=%D0%BD%D0%BE%D0%B2%D1%8B%D0%B9%20%D0%B3%D0%BE %D0%B4%20%D0%BA%D0%B0%D1%80%D1%82%D0%B8%D0%BD%D0%BA%D0%B8&stype=image&noreask=1&lr=194

A regular paperclip can also be triangular. http://images.yandex.ru/yandsearch?text=%D0%BD%D0%BE%D0%B2%D1%8B%D0%B9%20%D0%B3%D0%BE%D0%B4%20 %D0%BA%D0%B0%D1%80%D1%82%D0%B8%D0%BD%D0%BA%D0%B8&stype=image&noreask=1&lr=194

There used to be triangular boxes http://images.yandex.ru/yandsearch?text=%D0%BD%D0%BE%D0%B2%D1%8B%D0%B9%20%D0%B3%D0%BE%D0 %B4%20%D0%BA%D0%B0%D1%80%D1%82%D0%B8%D0%BD%D0%BA%D0%B8&stype=image&noreask=1&lr=194

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Prepared work: teacher 7 cells. "A" Vereshchagina Anastasia Checked the work: mathematics teacher Malyukina P.V. Triangle Project

In our life, many of the objects around us very often remind us all of a well-known figure, a triangle! So let's see where we can see it..

Cake - very plausibly resembles the shape of a triangle !!!

The bell also has a triangular shape!

Thermometer.

Even some flowers also look like a triangle

Children's application - Christmas tree

Furniture-table

Windows of the house.

Children's mosaic

Wrist watch

Bijouterie

Fixtures

All pictures for this work were taken from the site http://images.yandex.ru

(Something about ecological balance)

“And the locusts attacked all the land of Egypt, and lay down over all the land of Egypt in great numbers; before there was no such locust, and after this there will be no such.”

This is a description of only one of the "ten plagues of Egypt", which, according to the first book of the Bible "Genesis", the Lord God sent to the country of the pharaohs as a punishment for disobedience to his will. And before the invasion of the locust, Sabaoth first turned the water in all Egyptian rivers into blood, which killed the fish in them, then sent hordes of toads, clouds of midges, dog flies and an epizootic pestilence that mowed down all the Egyptian cattle (Fig. 1-5) ).

Law of balance

Certainly these biblical legends, for all their allegoricalness, nevertheless have a very real basis. Common to all such invasions is the sudden and sometimes catastrophic for people appearance in a relatively small area. huge amount any living organisms. Of course, such suddenly appearing, monstrous in size accumulations, for example, of the same locust, devouring all the vegetation on its way, seemed to people of all times and peoples a punishment for their sins sent from above. Neither the true causes of such outbreaks of numbers, nor the ways to prevent them, mankind did not know some one hundred and fifty years ago. And to a serious study of the relationship of the organism and external environment, factors influencing the abundance in nature of a particular species, science actually began only in the twentieth century. In the first third of the 20th century, scientists had at their disposal extensive data on mass reproduction in certain years of forest and forest pests. Agriculture, including in the Middle Volga region.

For example, it was found that fluctuations in the number of many terrible enemies of the forest are subject to a kind of "law of outbreaks". These include unpaired, willow and ringed silkworms, as well as their relative, the goldtail butterfly (Fig. 6-11).

How terrible they are, such facts speak. Huge areas of forests in Samara and some adjacent districts of the Simbirsk province in 1892-1893 were affected by the gypsy moth. Then his hairy caterpillars completely ate the leaves on the trees, and in some places (for example, at the Pachelma station, now the Penza region) they even delayed trains: the wheels of the locomotives slipped, crushing the caterpillars crawling across the railway track. A similar picture was repeated in 1933, when the area of ​​forests affected by gypsy moth only in the territory of the Middle Volga Territory amounted to 25 thousand hectares. And in 1935, its caterpillars completely ate the foliage in the eastern part of the Samarskaya Luka and on the left bank of the Volga around Kuibyshev.

The locusts did not disregard our region. From its invasions, three-quarters, and in a number of places - and completely perished crops of grain crops in the northern part of the Samara province and in the south of Bashkiria in 1912-1914, in 1921-1924, 1932-1935. But at the beginning of the 21st century, locusts also did not leave our region with their attention. Here is the message from the Ministry of Agriculture Samara region dated June 10, 2011:

"AT current year in the Samara region, there are favorable conditions for the development of especially dangerous pests, including locusts. This was announced by the Ministry of Agriculture and Food of the region.

An increase in the number of locusts is expected on an area of ​​approximately 23,000 hectares in Alekseevsky, Bezenchuksky, Borsky, Volzhsky, Kinelsky, Kinel-Cherkassky, Krasnoarmeysky, Neftegorsky, Pestravsky, Privolzhsky, Sergievsky, Stavropolsky, Syzransky, Khvorostyansky, Chelno-Vershinsky and Shigonsky districts.

According to operational information, as of June 9, hatching of locust larvae was noted in the places of overwintering of egg-pods on inhospitable areas and pastures exceeding the threshold of economic damage. The area of ​​such places in the Bezenchuksky district is 1.4 thousand hectares, in Khvorostyansky - 1.3 thousand hectares. In these areas, chemical treatment of crops affected by pests is organized. More than 700 hectares have been cultivated in the Khvorostyansky district. In Bezenchuksky - 600 hectares. In the Neftegorsk region, the exceedance of the threshold of economic damage for locusts was noted by 2 hectares. This area was promptly subjected to chemical treatment, the source of the spread of pests was eliminated.

So what is it that sometimes happens in nature? What mechanisms sometimes open a giant invisible bag to release voracious hordes of various vile creatures from there? And is it possible at all, if not to prevent, then at least to predict for the coming seasons such a catastrophic outbreak of their numbers?

Experts say that all this is quite possible. Each of us, even without being a biologist, knows that all organisms have the ability to reproduce their own kind, and the possibilities of reproduction under favorable external conditions can be truly unlimited. So, the offspring of many types of microorganisms that divide every two to three minutes, in the presence of nutrients capable of covering the entire surface of our planet with a meter layer in just 10-15 hours. And even a couple of the most ordinary field sparrows could produce about 275 billion (!) of the same gray chirping birds over the course of ten years.

But, of course, in real nature, this will never happen. The unrestrained reproduction of living organisms is limited by environmental factors, primarily the amount of food in a particular area of ​​the biosphere. Thus, a kind of equilibrium in the number of any species arises, similar to the equilibrium of a pendulum. On the one hand, this pendulum sets in motion the ability of organisms to increase their numbers, on the other hand, it is pushed into reverse side environmental factors limiting this number. Therefore, as biologists say, although the number of individuals of any species in a given population is in balance with their environment, this balance will always be mobile, dynamic. The pendulum of numbers is constantly swinging in both directions from the point with the most favorable environmental conditions for this species, forming special “waves of life”. The period of these waves, under constant external conditions, will always be almost the same.

And therefore, having studied well for many years the rhythm of outbursts of numbers, for example, the same gypsy moth, knowing the parameters of its habitat for the season of interest to us, it is possible to predict the time of mass reproduction of the pest with an accuracy of up to a year. Actually, forest protection specialists knew how to do this back in the thirties of our century. So, scientists predicted in advance an outbreak of gypsy moth in the Middle Volga region in 1933-1935. This outbreak was "prepared" by previous jumps climatic conditions- in summer, several seasons before it, severe droughts hit the region, and in winter - severe frosts. The weakened forests created a favorable environment for a sharp increase in the number of silkworm caterpillars.

However, in such a pure state, the “waves of life” in many species turned out to be almost impossible to detect. The fact is that now on the surface of the planet you can hardly find a corner where human activity would not affect to one degree or another. In modern conditions, it has become the most powerful factor in the external environment, sometimes radically influencing the abundance of the vast majority of animal and plant species.

This is very clearly seen in the classic example of the forest trinity: vegetation - ungulates - large predators. For the Samara region, the most typical organisms standing at the vertices of such a triangle are usually, on the one hand, forests, on the other, elks, and on the third, wolves (Fig. 12-14).

The connection between the “tops” of this by no means love triangle is clear in principle. Elderly feed on forest woody vegetation, and when there are too many of them, the elk food base is too undermined and gradually degrades. But at the same time, the high number of forest giants is very favorable for wolves - finding large food supplies in the face of moose, predators also begin to multiply intensively, cut more and more elk, and this sharply reduces their number in this population. In the meantime, the forest has the opportunity to "heal the wounds" inflicted by ungulates, to restore its individual sections, united and broken by them. But at the same time, the size and number of wolf packs are irresistibly falling: now the predators have already undermined their food base, and therefore ruthless natural selection begins to eliminate all unnecessary individuals, primarily the weak and unadapted, leaving, as expected, the strongest and smartest wolves. Moose, left without pursuers, again begin to feel more and more at ease, multiply almost unhindered among the forest thickets, and the history of the trinity begins its new cycle.

Well, what about man? In the described triangle, he most often appears, and mostly very successfully, as a serious competitor to the wolf. After all, for all of us, perhaps, moose meat for a meal would be no less desirable dish than for wolf pack. And, it would seem, here it becomes clear to anyone: if you want to increase the number of moose in the forest, take a gun and go to exterminate all the malicious wolves who dare to eat this most beautiful, smartest, but also - to be honest - a very attractive animal for us, with a gastronomic of course point of view. However, everything is not so simple. Usually, going with a gun to protect the moose, people forget about the third vertex of the triangle ...

In order to get material for reflection on the topic "The relationship between the forest and the elk", it is necessary to cite several facts from Russian history.

It is usually believed that in the old days, about two or three hundred years ago, there were a lot of animals in our forests, especially in sparsely populated areas. For successful hunting, modern guns were not needed - with the abundance of that time, they say, a horn and a knife were enough. However, this is not the case. For example, even under Peter I, in 1720, the Military Collegium received the highest decree. To sew ammunition from elk skin for forty thousand soldiers, it was necessary to get the corresponding number of elks in the forests. Procurers could not fulfill the royal command: they could not get more than two and a half thousand elk skins a year. So a third of all dragoons had to be dressed in goatskin, and the infantry in cloth.

It turns out that in those days the elk were rare? This, in general, is not surprising. It’s just that in the era of Peter the Great, in conditions of almost untouched nature, there were just as many of them as the forest could feed, while the excess of elk was quickly “taken off” by predators. This situation remained virtually unchanged until the second half of XIX century, when the scale of wolf hunting in our country sharply increased. At the same time, due to increased deforestation for industrial and domestic needs, huge spaces appeared in Russia, which, instead of tall trees or tree growth, turned out to be covered with either low shrubs or even weeds. Meanwhile, such vegetation is a favorite dish for moose and at the same time an excellent shelter for the animal; therefore, a sharp outbreak in the number of moose in late XIX centuries throughout European Russia. It was then that hunters of all ranks took up them - from counts to bastard peasants; joint efforts during the first fifteen years of the twentieth century destroyed almost all the forest giants in the territory from the western borders of Russia to the Urals. By the way, by Lenin's decree "On the timing of hunting and the right to hunting weapons", adopted in May 1919, elk hunting was completely banned in the entire European part of Russia (Fig. 15-17).

The measures taken by the Soviet government did their job. After the civil war, the number of elk animals began to increase steadily everywhere, and by the 40s they had already ceased to be rare animals, for example, in the Zhiguli Reserve. The elk population decreased somewhat during the years of the Great Patriotic War, when there were no wolf hunts almost anywhere, and there were a lot of wolves throughout the country. When, after the war, the predator was taken up again, the moose quickly multiplied again. According to the State Hunting Inspectorate, in the 1980s, about two thousand moose were registered on the territory of the Kuibyshev region.

It is estimated that in a year one forest giant consumes on average about seven tons of forest gifts: four tons of tree shoots, one and a half tons of foliage, 700 kilograms of bark, the rest is grass, shrubs, mushrooms. Out of a hundred trees, he completely destroys ten and seriously damages seventy, only twenty of them are intact. Moreover, a curious fact is observed: a group in which there are more than three elk, passes no more than two hundred meters per day; elk alone is about ten times more mobile.

Based on their research, scientists derive numbers - how many moose can the forest endure? (Fig. 18-20).

However, the data of different authors turn out to be very contradictory: foresters insist that no more than five elks eat on a thousand hectares, and in some types of forest (for example, in oak forests) - no more than one. Hunters, on the other hand, believe that it is possible to breed elk and up to ten, or even thirty, per thousand hectares of forest. Perhaps, the data of foresters, as people who, on duty, are interested in protecting the country's green cover, should be recognized as more reasonable. After all, game managers most often operate with average figures, while the above data were given on the extremely uneven distribution of elks over the forest area, and therefore in some places their concentration can reach such values ​​that the forest is almost devoured by them.

The significant overpopulation of our forests with elk is clearly seen from the results of studies conducted in the Zhiguli Reserve for 10 years (from 1970 to 1979). The staff of the reserve studied the causes of moose mortality in winter.

The figures turned out to be very eloquent: 10 percent of all moose died from diseases and injuries, 14 percent from wolves and feral dogs, the same number of moose died from a poacher's bullet, half as much (seven percent) from a collision with cars on the Zhigulevsk - Shiryaevo road. The rest of the moose (more than half - 55 percent) died from exhaustion in the winter without food. At this time, all the vegetation available to them was already eaten, and because of the deep snows of the Zhiguli, it was impossible for moose to reach other trees and shrubs.

And here pay attention to one more circumstance. Usually, at the end of each spring or at the very beginning of summer, central and regional newspapers begin to be full of headlines like “Walking along the elk street”, “Forest guests”, “Clash with an elk” and even often, as a sad result, “Drama without hunting”. The topic of such articles is the same from year to year: moose enter settlements, even the centers of large cities, die under the wheels of cars, or are smashed to death against some fence, driven here by a crowd of curious townspeople. But after all, from a good life, moose cows penetrate busy streets: the fact is that just at this time, moose cows drive away last year's grown-up calves from themselves. And those, not finding good fodder sites in the forest already eaten by his relatives, rush straight to the untouched by elks, but very crowded city squares and parks ...

All these facts speak of one thing: having assumed the role of a regulator of the elk population, a person almost nowhere managed to fully replace the wolf in this food chain. By this, he began to inflict damage ... on the elks themselves, who were dying from meeting with civilization on the roads and in settlements.

But what about the wolf? How should we treat him now? On this score, there are directly opposite opinions: some believe that the wolf must be destroyed by all means, others are convinced that this predator is everywhere necessary and useful. The truth, apparently, as always, lies in the middle.

Robber or orderly?

Back in the late 60s - early 70s of the twentieth century, this dilemma was confidently resolved by many zoologists in favor of the second premise: "The wolf is the orderly of the forest." But, however, years passed, and the ranks of the defenders of the "gray robber" gradually melted.

Yes, yes, that's right - a "gray robber", and not at all a "forest orderly", who the wolf was quite recently, in the mid-70s. And this nickname, perhaps, for him is one of the most flattering (Fig. 21-25).

In 1980, in the Pokhvistnevsky district, I had a chance to talk with those who either quite shortly before met with wolves, as they say, face to face, or saw traces of their robbery. For these people, there was no problem who the wolf was - a pirate or an orderly. I did not even dare to ask the narrators on a similar topic - they would not understand me, to put it mildly.

According to official data, in the late 1970s and early 1980s, several cases of wolves attacking people were recorded in the same Pokhvistnevsky district. One of them ended tragically for a person.

What happened? Why did the “forest orderly” suddenly regenerate so dramatically? After all, this change took place literally over a dozen years. And in such a short period of time, neither the biology nor the behavior of the predator could change radically. And, of course, his wolf essence, so well known to all of us from children's fairy tales, remained with him. Consequently, the origins of this "rebirth" must be sought not in the wolf, but in the changed attitude of man to the wolf, that is, in ourselves.

Of course, it was not the propaganda campaign in defense of the “orderly” that was the main reason why the number of the predator has recently jumped sharply (according to the state hunting inspection, at the beginning of 1985, at least 200 wolves lived in the region, and this is a lot). In the mechanism of nature, the decisive factor influencing the number of individuals in a population of a particular species is food, and in the 70s there was plenty of it for wolves throughout the country. At this time, there was an interesting outbreak of the number of wild ungulates: as already noted, about two thousand elk alone lived on the territory of the Kuibyshev region. Livestock breeding complexes and enterprises where the rules for carrion burial were violated have become a very important source of food. Of course, poachers also contributed to the prosperity of wolves, who, hunting ungulates, left a lot of wounded animals in the forest. And, finally, even the hunters themselves, who often ecologically illiterate settled deer, roe deer, pheasants, beavers and other imported animals in various areas of the region, in fact, supplied easy prey for the “gray robbers” to the hunting grounds. Acclimatized animals, finding themselves in an unfavorable, unusual environment for them, quickly died either from starvation or in the teeth of predators, and an incorrect, scientifically unfounded "resettlement" only brought a double loss to the state.

The wolf is one of the most common mammals not only in our country, but throughout the world. Within the USSR, it is absent only on some islands in the Arctic and Pacific Oceans. Contrary to popular belief, the wolf is by no means a forest animal; it prefers open spaces. In the vast territories of the deaf Siberian taiga, these predators are practically absent. The taiga regions cannot provide enough food for the wolf, especially in winter when deep and loose snow falls. But in the snowless areas of the forest-steppes, predators feel very at ease.

Of course, the role of the wolf in nature, like any other species, cannot be only negative or only positive - always, in any area, in the activities of a wolf pack, you can find both sides. The whole difference is only in understanding the correct ratio of usefulness or harmfulness of a wolf in a given situation. So, for example, the positive influence of predators on populations of wild ungulates has been indisputably proven - here is its selective activity, that is, the culling of unadapted, weak individuals, and indirectly improving the condition of the forest.

Some opponents of the wolf believe that without him in wild nature it is quite possible to cope - the wolf role, they say, will be successfully performed by hunters. After all, they, too, can remove from the population exactly as many animals as necessary to maintain balance (Fig. 26-28).

This example clearly shows how simplistic some "specialists" sometimes understand the most complex relationships in nature. This applies even to such a seemingly small chain as “elk - wolf - forest”. At the same time, they forget that only in-depth painstaking research can reveal at least the main aspects of any natural connection, not to mention the sides of the secondary and tertiary, and others that are at an even lower level. In order not to be unfounded, we will give some examples of such inconspicuous aspects of the "wolf - elk" connection.

As you know, weakened, non-viable animals go to the table for wolves first of all. However, a physically strong elk can become their prey if it turns out to be unintelligent, stupid, to put it simply. In addition, wolf teeth also kill most of young ungulates - here there is no need to talk about any physical strength, and therefore only elk calves survive, having superiority in intelligence, cunning. As we can see, wolves select ungulates not only according to physical, but also according to intellectual data.

In addition, it was noted that with a significant press of wolves on the population of elk, the fecundity of the latter noticeably jumps up - the number of twins born increases almost one and a half times. Thus, wolves also change the ratio of age groups in ungulate populations. Unproductive individuals become their victims, as a result of which more food remains in the biocenosis, and in mature, physically and intellectually full-fledged moose, living conditions improve and fertility increases.

And what about the hunters? Can they really perform at least some of the mentioned "wolf" functions in the moose population? Let's figure it out.

It is difficult for hunters to maintain the quality of the population even at the current level, if only because a person has a limited ability to correctly assess even the physical, and even more so the intellectual state of the animal, the correspondence of its behavior to living conditions. How long does a shooter usually see an elk? A matter of seconds. If you were at least three times a specialist, but how can you determine any deviations of an elk from the norm in these insignificant moments?

One more circumstance. What animal is the hunter most interested in getting? That's right - to be as large as possible. After all, the size of the prey is not indicated in the license, and therefore the most healthy, large moose, capable of leaving full-fledged offspring, just become the victim of a hunting shot. But if wolves were in the place of a man, a strong animal would easily deal with them - an elk, standing backwards in a dense bush or in an impenetrable windbreak, successfully defends itself with sharp hooves from a whole pack of wolves.

And even if we assume that the elk fishing will go perfectly - only weak, defective and stupid animals are shot back, everyone gets wounded animals, then this will also not be enough for a full replacement. After all, predators are like a tool natural selection, "train" the physical form and intelligence of ungulates, ultimately guiding their evolution. A person cannot do all this.

As a result, we came to a situation where, every year, more and more cases of a sharp deterioration in the state of deer, elk, and wild boar populations began to be recorded in hunting farms, where selection was carried out only by humans. Animals became smaller, died in masses due to infections, due to weather conditions- in a word, for reasons that in normal circumstances do not cause such environmental disasters.

However, on the other hand, the defenders of the wolf very often forget that everything described applies only to wild, untouched nature. In a well organized hunting the wolf is not only unnecessary, but very often harmful. After all, wild boars, deer and elk, which are bred and fed here, are almost domestic animals. And it is completely ecologically illiterate, even just ridiculous to talk about the selective role of the wolf in animal husbandry.

Without a doubt, the fight against wolves must be waged. But at the same time, as already mentioned, it is necessary to clearly distinguish between wolves of untouched nature and wolves living off domestic animals. In fact, these are two different, sharply different ecological forms of a predator.

However, some may think that the author of the book is a sworn enemy of the entire wolf family. Not at all. He simply traces a curious pattern: when someone begins to overly defend the wolf, then such a defender completely forgets about the third peak of the forest triangle mentioned above. Let's say even more: the author of the book believes that the opinion that is quite common now, especially among hunters, is fundamentally wrong, the essence of which boils down to the following: "Wolves do not need to be studied, wolves must be exterminated." No, they need to be studied, if only because in order to fight it more successfully. Completely exterminate this smart, beautiful and strong beast, of course, it is not necessary, and perhaps impossible. The wolves left again in small numbers after intensive hunting for them will indeed become the breeders of the forest, a necessary link in the great chain of life.

Like any other vertex in our triangle, the wolf is an inseparable part of it. And therefore, everyone who undertakes to boldly reshape the system of natural connections must definitely remember one very simple thought: this triangle is good precisely in its trinity, and either the elimination of one of the peaks or its excessive protrusion will be a real ecological disaster for the entire community. And such a harmonious combination of all the relationships of organisms among themselves is the main condition for the great natural balance (Fig. 29-31).

Valery EROFEEV.

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GOU RK "S (K) Sh No. 45", Ukhta

Educational project

mathematics

I've done the work

5b grade student

Zhakheev Gavril

Supervisor

Polyakova T.A.

Ukhta

2016

Introduction

Since childhood, we have known such figures as a triangle, a circle, a square. And it would seem that there is nothing surprising in them. But in fact, this is a misconception.

In the 5th grade, in geometry lessons, we got acquainted in detail with a geometric figure - a triangle. It turned out that we did not know much.

In order to learn even more about this figure, we decided to do a little research. Our parents and school teachers helped us in this.

SLIDE 2

We have set ourselves the following questions to which we would like to receive answers:

1) what triangular objects surround us

2) what properties of a triangle are applied in Everyday life

3) what puzzles are associated with triangles

Most main question- Can a triangle be called an important figure?

We asked the teachers and students of the school to answer it.

SLIDE 3

11 students and 8 teachers interviewed

Question: Do you consider the triangle an important figure?

As you can see, the majority of respondents do not consider the triangle an important figure. We will try to prove otherwise.

Question 1. What is a triangle?

SLIDE 4

The term "triangle" has different meanings:

In mathematics, it isgeometric figure bounded by three mutually intersecting straight lines forming three internal angle

In drawing - a ruler in the form of such a figure, which is used for drawing

In music, a percussion instrumentfrom a steel rod, which is struck with a metal stick

In everyday life - a type of relationship between three people

In our work, we take only the first value - the mathematical one.

Question 2.How did triangles originate?

SLIDE 5

How exactly the triangles appeared is unknown. But geometry was discovered by the Egyptians, and arose when measuring the Earth. The floods of the Nile River washed away the boundaries of the plots, and people had to re-mark the fertile sections of its banks, from which the water had gone. The simplest was a plot in the shape of a triangle.

Question 3. Where do triangles meet in our lives?

SLIDE 6

In our life, the triangle is found everywhere, you just have to look closely. Here are the answers of teachers and students to our second question: where does the triangle meet in your life?

House Roof Bicycle Spruce

On clothes Sail Road signs

Home Interior Labor Training Lessons Baking

There are also other triangular objects.

front triangle

SLIDE 7

White flocks of letters flew to Russia.
They were read with excitement, they knew them by heart.
These letters are still not lost, not burned.
As a great shrine to the sons they protect.

These lines are dedicated to the front-line letter.

Since there were not enough envelopes during the Great Patriotic War, the soldiers wrote letters on a plain sheet of paper folded into a triangle. Send these emails for free.

Relatives were looking forward to triangular news from the front. The letter about the death of a soldier came in an envelope.

In memory of the heroic soldiers - defenders in the Battle of Stalingrad, a memorial complex "Soldier's Field" was built near the Volgograd - Moscow road. An urn with the ashes of fallen soldiers was buried in a mass grave. Nearby is a sculpture of a girl with a flower in her hand. Nearby is a marble triangle of a soldier's letter.

On this memorable triangle is a letter from Major D. Petrakov to his daughter, written on September 18, 1942 after the battle: “My black-eyed Mila! I am sending you a cornflower. suddenly another explosion - the cornflower was torn off. I picked it up and put it in the pocket of my tunic. The flower grew, reached for the sun, but it was torn off by an explosive wave, and if I had not picked it up, they would have trampled it. This is how the Nazis act in occupied settlements where they kill the guys. Mila! Papa Dima will fight the Nazis until last breath so that the Nazis do not treat you the same way as with this flower ... "

Road signs

SLIDE 8

Many of us would like to become drivers in the future.

In this case, we will definitely need to know the road signs. There is a group of road signs in the shape of a triangle. What do they mean?

Road sign in the shape of a triangle on a white background with a red border - about something warns. They are installed in a city or village for 50-100 m, outside locality 150 - 300 meters to some site.

Origami

SLIDE 9

In the 4th grade, the guys in our class attended the Origami circle. Origami is the ancient art of paper folding. The basis of crafts are the basic forms. Two of them are a triangle and a double triangle.

Based on these forms, you can make different crafts:

The modular origami is especially beautiful. These products have their own peculiarity - they are assembled from a large number of small origami blocks.

The parts are put into each other, which is well fixed and the product does not fall apart.

Question 4. What puzzles are associated with triangles?

SLIDE 10

The Bermuda Triangle is an amazing area of ​​the western part Atlantic Ocean. This place is also called anomalous zone. Place mysterious disappearance ships and aircraft.

At the lesson of natural history, the teacher Troshina N.M. she told us about this phenomenon and showed us on the map where this mysterious place is located.

This region is not easy - there are many shallows, a huge number of fast water and air currents, cyclones often arise and hurricanes rage. Another reason for the huge number of accidents, experts call the ability of the ocean to produce infrasound signals that cause panic among the crew, because of which people can even throw themselves overboard.

Despite the excitement raised around the Bermuda Triangle, scientists argue that in reality this territory is no different, and a large number of accidents are mainly associated with severe natural conditions.

Question 5. Why is the triangle used in construction?

SLIDE 11

In the process of studying the topic, we learned that a triangle has such a property as rigidity. Consider models of two figures - a triangle and a quadrilateral.

Under the influence of a small force, the quadrilateral changed its shape, but the triangle did not. This is because the triangle is a rigid figure.

This property of the triangle is used in construction.

conclusions

In the course of our research, we came to the conclusion that the triangle is indeed an interesting and important figure. The world of triangles is diverse. A person is surrounded by many household items, clothing, musical instruments having a triangular shape. The triangle has been used by man from ancient times to the present day. This is the only figure that has the rigidity property.

SLIDE 12

Applications can be made from triangles, they can be embroidered, knitted.

We hope that the interviewed teachers and students of our school, who believe that the triangle is not an important figure, were convinced that they were wrong and changed their minds.

We already know what a triangle is, its types according to the lengths of the sides and the type of angle. We are able to build a triangle on known sides with the help of a compass. But this is not all knowledge about the triangle. There are many more discoveries ahead of us.

Eretin Artyom Olegovich,

3A grade student

Supervisor

Kasyugina Maria Ivanovna,

primary school teacher

MBOU "Novinskaya School"

Introduction

I am in class 3A. In the lessons we learn a lot of new and interesting things. But there are some things that, it seems to me, it is not necessary to study at all. Because it is not clear where later this knowledge can be useful to you. For example, we studied letters. It is necessary to write and read. We have studied the numbers. It is necessary to count. I love mathematics very much: examples, problems. But I don’t understand at all why we need to study figures. Circle, still not going anywhere. These are the wheels of the car, the planets, the solar system, the gears are different in the construction of robots. But the triangle, in my opinion, is completely unnecessary.

Object of study: geometric figure "triangle"

Subject of study: the use of triangles in the surrounding life.

Purpose of the study: find out how you can use the geometric figure "triangle" in the surrounding life.

Tasks:

1. Find out if a triangle is needed in my family's life.

2. Conduct a survey of parents and testing classmates.

Hypothesis:the triangle is a peculiar figure, practically inapplicable in the world around me.

Study methods:

· Measuring works of construction objects

· Testing classmates

Parent survey

· Photographing

Part one. Dad's look at triangles. Construction.

At the beginning of my research, I turned to my father.

He told me that triangles are very widely used in construction. And when he built our house, this knowledge was very useful to him. (Appendix 1. Photo 1-3)

It turns out that even in ancient Egypt, when building buildings, people came up with the idea of ​​using a triangle. Then they did not have modern measuring instruments, as they do now, and they used a rope. On these ropes at equal distances from each other, the Egyptians tied knots. If it was necessary to build a building with right angles, they took a rope with four knots, a rope with five knots and a rope with six knots. Then they built a triangle on the ground with sides of three, four and five equal segments, thanks to these ropes. Thus, one absolutely right angle was obtained.

And if you attach the same inverted triangle to this triangle, you get an even rectangle. This method is still used in construction today. It is called the “Egyptian triangle method” (Appendix 1. Photo 4)

Also, the triangle is the most rigid figure. This property is widely used in roof construction. Long rafters are additionally reinforced with diagonals. The longer the rafters, the more triangles are required. The result is a single rigid structure that can withstand heavy loads. The same method is used in the construction of other structures. (Appendix 1. Photo 5-6)

Also, the triangle is the most stable figure. A stool with three legs will never stagger, but will stand steadily on any surface. Therefore, all tripods for cameras and various measuring instruments are made with three legs. (Appendix 1. Photo 7)

It turns out that there are a lot of triangles that surround me, these are almost all the roofs of houses. (Appendix 1. Photo 8)

Conclusion 1. Triangles have been used in construction for a long time. They also came in handy for the construction of our house.

Part two. Mom's look at triangles. Psychology.

Then I turned to my mother and asked her how the triangle figure could help her.

Mom told me that there is such a psychological test, where you can determine the qualities of a person by geometric shapes. Mom suggested that I take this test in class and find out who in our class are "triangles". (Appendix 1. Photo 9)

For the test, I needed geometric shapes: a square, a rectangle, a circle, a triangle and a zigzag. (Appendix 1. Photo 10)

The children had to choose any figure they thought they looked like and draw it. (Appendix 1. Photos 11-12)

Then I deciphered the meaning of these figures and told the guys about their qualities. Everyone was surprised how you can determine that they are inquisitive, purposeful, friendly or restless just by one geometric figure. Maria Ivanovna, my class teacher, confirmed that all the guys chose the figures correctly, they fit them perfectly.

And as a result of testing, I found out that I am surrounded by two "triangles" in the class.

Conclusion 2. Triangles help in mother's work.

Part three. Children's view of triangles. "Triangle Coloring".

There is also my younger brother Kirill in our family, he will soon go to first grade. I thought, why does he need triangles.

It turned out that when preparing for school there are a lot of tasks with geometric shapes, including triangles.

The performance of such tasks develops spatial thinking, logic, imaginative thinking and even creativity. (Appendix 1. Photos 13-14)

I decided to help my brother practice doing these tasks and drew my "triangular" coloring book for him. (Appendix 1. Photo 15)

Kirill completed the task correctly and showed imagination by turning an ordinary dog ​​into Superman's dog! (Appendix 1. Photos 16-17)

Conclusion 3. Triangles help kids get ready for school.

Conclusion

I really enjoyed exploring the triangles. It turned out to be very interesting. Triangles are all around us.

My hypothesis that the triangle is practically inapplicable in the outside world was not confirmed.

Triangles are needed by both adults and children. Triangles are used in education, psychology, and construction.

I liked measuring and calculating. During my research, I

· learned about the "Egyptian triangle",

· found out what a rafter is,

· learned how to test and process results,

· tried his hand at creating geometric patterns.

It turns out that the triangle and its properties are still being explored by scientists. And I still have to meet with a triangle at school on a very interesting subject - geometry. I think this will be one of my favorite items.

Bibliography

1. Zakharov Yu.A. Psychological tests. M. 2014

2. Salmin. We learn to think. What goes with what. M.2016

3. Tests for preschoolers. M 2015

Internet resources:

1. www.wikipedia.org

IN THE WORLD OF TRIANGLES

The project was prepared

7th grade students

Gaisaeva F., Epishina A.,

Morenkova V.

Relevance

• The triangle is one of the simplest shapes in geometry. Is it so? Does the triangle have any other secrets? Are triangles necessary in life?
• The topic "Triangles" is one of the first and most important topics in geometry for seventh graders. The further success of students in geometry depends on its deep study. With this project, we want to emphasize the importance of the topic, to develop children's interest in the subject of geometry.

Objective of the project:

Find out what role triangles play in our lives, where we meet them and whether we always notice them.

Project objectives:

1. Why study the properties of triangles?

2. What role do triangles play in human life.

3. Can triangles protect a person.

It may not be for nothing that the triangle was used as a talisman in many ancient cultures and was very symbolic.

• The triangle is the first mystical geometric figure. The triangle was used in ornaments by the ancient peoples. For example, in ancient Egypt, he was the embodiment of spiritual will, higher intelligence and love - the triad. It is also a symbol of the triune nature of the Universe, which can be classified as follows:

• sky, earth, man;
• father, mother, child;
• man as body, soul, spirit;
• mystical number 3, three, the first of the flat figures.
• This is how the surface symbol was born. The surface itself is made up of triangles. Even the termination symbol is an equilateral triangle. In the Ancient East, the triangle was considered a symbol of the nature of everything true. Two triangles connected by vertices were considered the emblem of the time cycle.

Conclusions:

• Triangles are not at all a rare geometric figure.
• Man has studied its properties since ancient times. This helped him in construction, solving the needs of land surveying and military affairs.
• Thousands of years ago triangles were used for amulets. Now knowledge helps us to protect ourselves, and here again we cannot do without triangles.