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» Diameter from circumference formula. How to find and what the circumference will be equal to. Determining the perimeter of a circle

Diameter from circumference formula. How to find and what the circumference will be equal to. Determining the perimeter of a circle

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In any community there are always social norms accepted in a given society, according to which it lives. Deviation from these norms or non-compliance with them is called social deviation or deviation.

Social norms are requirements, instructions and expectations of appropriate behavior. The emergence and functioning of social norms, their place in the socio-political organization of society are determined by the objective need to streamline societies and relationships.

The emergence of social norms is based, first of all, on the needs of material production. The repetition of acts of production, distribution and exchange require the presence of such general rules, which would allow participants in the relevant societies and relationships to regularly and uniformly enter into these interactions. Social norms, therefore, embody an abstract model of these interactions, enabling individuals to anticipate the actions of other participants in societies and relationships and build their own behavior accordingly.

Social norms, regulating people's behavior, regulate a wide variety of relationships. They form a certain hierarchy of norms, distributed according to the degree of their social significance. Firstly, they promote social integration. Secondly, they serve as unique stages of behavior, a kind of “instructions” for individuals and social groups performing separate roles. Thirdly, they help control deviant behavior. Fourthly, they ensure the stability of society. Based on the nature of regulation of social behavior, a distinction is made between norms - expectations and norms - rules. The first of them only outline the framework of socially approved behavior. Violation of them causes disapproval from society or a social group, but does not entail any serious sanctions. The norms belonging to the second group are characterized by a greater degree of severity. They define the boundaries of acceptable behavior, as well as activities that are considered unacceptable and therefore prohibited. Violation of such norms entails the application of serious sanctions, for example, criminal or administrative. Based on areas of activity, norms can be divided into group norms, which operate on the scale of one or several groups, and universal norms, which operate on the scale of the entire society.

Norms form habits, customs, and traditions. In the majority modern societies the most important and significant norms acquire legal status and are enshrined in laws.

Social norms are acquired by an individual in the process of socialization. Behavior that corresponds to certain norms in society is designated as conformist. In contrast to conformist behavior, there is deviant or deviant behavior.

The normative systems of society are not fixed, forever valuable. The norms themselves change, and attitudes towards them change. Deviation from the norm is as natural as following it. At all times, society has tried to suppress undesirable forms of human behavior. Sharp deviations from the average norm, both positive and negative negative side threatened the stability of society.

In most societies, control of deviant behavior is asymmetrical: deviations in the bad direction are condemned, and deviations in the good direction are approved. Depending on whether the deviation is positive or negative, all forms of deviation can be placed on a certain continuum. At one pole there will be a group of people showing the most disapproved behavior, at the other pole there will be a group with the most approved deviations.

Any behavior that causes disapproval public opinion, is called deviant. This is an extremely wide class of phenomena: from ticketless travel to the murder of a person. IN in a broad sense deviant - any person who has gone astray or deviated from the norm. Forms of deviant behavior include criminality, alcoholism, drug addiction, prostitution, gambling, and suicide.

In a narrow sense, deviant behavior also means deviations that do not entail criminal punishment and are not illegal.

A detailed sociological explanation of deviation was first given by the French scientist E. Durkheim. He proposed the theory of anomie, which reveals the significance of social and cultural factors. According to Durkheim, the main cause of deviation is “lack of regulation,” “normlessness.” Essentially, this is a state of disorganization of society, when values, norms, social connections are either absent or become unstable and contradictory. E. Durkheim considers deviation to be as natural as conformism. Moreover, deviation from norms carries not only a negative, but also a positive beginning. Deviation confirms the role of norms and values, and gives a more complete understanding of the diversity of norms. The reaction of society and social groups to deviant behavior clarifies the boundaries of social norms, strengthens and ensures social unity. Deviation promotes social change, reveals an alternative to the existing one, and leads to the improvement of social norms.

The American sociologist S. Merton, who substantiates this theory, believed that deviation occurs when there is a gap between the goals of society and at the same time the means to achieve them.

According to the outstanding modern sociologist T. Parsons, anomie is “a condition in which a significant number of individuals are in a position characterized by a serious lack of integration with stable institutions, which is essential for their own personal stability and the successful functioning of social systems.”

The basis of psychoanalytic theories of deviant behavior is the study of conflicts occurring in the mind of the individual. According to S. Freud's theory, for each person, under the layer of active consciousness there is an area of ​​the unconscious. The unconscious is our mental energy, in which everything natural, primitive, not knowing boundaries. This biological entity a person who has not experienced the influence of culture. The main idea of ​​cultural theories of explanation of deviation (Seline, Miller, Sutherland, Claward) is conflicts between the norms of the subculture and the dominant culture. The theory of labeling (Becker) proceeds from the fact that deviance is a kind of label that some groups with power “attach” to the behavior of weaker groups.

Basically, all theories call deviant behavior that deviates from the norm with a minus sign. But in any society there are always people whose behavior is ahead of existing standards and is more progressive in comparison with them. This type of behavior is most characteristic of society during times of various social restructuring.

The above theories define different reasons, causing social deviations. There can be many of these reasons; they change with the development of society.

But the constant and main source of deviation, which makes this phenomenon objective and always characteristic of human society, is social inequality as unequal opportunities to satisfy needs.

Other sources and causes of social deviations include the following.

  1. When in the process of socialization by an individual of patterns of behavior, social norms and values, failures, failures, and shortcomings are allowed.
  2. Dysfunctional families. Numerous studies of youth crime have shown that about 85% of young people with deviant behavior were brought up in prosperous families. American researchers in the field of social psychology have identified five main factors that determine family life as dysfunctional: ultra-severe paternal discipline; insufficient maternal supervision; insufficient paternal affection; insufficient maternal affection; lack of cohesion in the family.
  3. Numerous cases of deviant behavior in completely prosperous families. Norms adopted from childhood can be revised or discarded during interaction with the surrounding reality, in particular with the social environment.
  4. Anomia (state of lack of norms). This happens in a constantly changing society, where there is no single and unchanging system of norms. In such a situation, it can be difficult for an individual to choose a line of normative behavior, which subsequently gives rise to the individual’s deviant behavior.

Thus, deviant behavior plays a dual role in society: on the one hand, it poses a threat to the stability of society, on the other, it supports this stability.

Social sanctions are used to monitor compliance with norms and values, as well as to prevent deviant behavior. Social control is understood as the normative regulation of people’s behavior and their relationships, ensuring self-regulation of the social system. Social control stimulates positive changes in society. The problem of the relationship between the individual and society occupies a central place in establishing social control. Theoretically, the relationship of society to the individual under conditions of social control looks quite simple: adjusting individual qualities to a social standard. In reality, relationships are complicated by the presence of individual consciousness in the individual, and, consequently, the ability to consciously evaluate, accept, reject or change stereotypes, norms and values ​​that are offered to the individual at the level public consciousness. Social control is carried out through the reaction of society, the social community to the individual behavior of the individual. There are many different sanctions in society. Some of them (legal sanctions) are strictly regulated, formalized and applied by authorized persons and power structures in accordance with the rules of law. Other sanctions (moral) are informal and are applied in the form of approval or condemnation. But full-fledged social control is a set of means and methods of influencing society on undesirable forms of behavior. Therefore, social control can be effective when its various mechanisms are used, taking into account the characteristics of the deviations themselves.

The approach and consideration of deviance, social control and the political regime in Russia requires special attention.

Russia has never been a democratic state, nor has it ever been a rule of law state. (Declaring it as such in Article 1 of the Constitution Russian Federation- at best, an advance with unclear prospects). In Russia, “neither the authorities nor the people have ever had respect for the law.” Extremely brief attempts at democratization in the context of history (the 60s of the 19th century, from February to October 1917, Gorbachev’s perestroika) ended with a return to the circles of absolutism, totalitarianism, and authoritarianism. The population of Russia has never lived in conditions of political freedom and respect for the rights of an independent individual. Moreover, as the famous “dissident” and human rights activist V. Bukovsky recently said: “we don’t even know whether the people want to live in conditions of freedom and democracy.” I’m afraid that “The Russia that we lost” was no better (not more democratic, not freer, not more civilized) than the one we created and have...”

Russia at the end of the nineteenth and beginning of the twentieth century is characterized by a relatively stable number and level (per 100,000 population) of registered crimes. Thus, the crime rate averaged 177 in 1874-1883, 149 in 1884-1893. “Echo” of the 1905 revolution, defeat in the war with Japan, the revolutionary situation of the beginning of the twentieth century. was reflected in the level of registered crimes: (1899-1905 - 229, 1906-1913 - over 270 annually).

More tragic is the practice of the totalitarian Soviet regime. From 1918 to 1953 More than 3 million 700 thousand people were convicted of “counter-revolutionary crimes”, of which at least 820 thousand were sentenced to capital punishment - execution. Only for the terrible years 1937-1938. 1 million 350 thousand people were sentenced for this, of which 682 thousand were sentenced to death.

End Stalin era did not mean the end of the totalitarian regime. All the features of totalitarianism were inherent in the Soviet government from October 1917 until Gorbachev’s perestroika.

Khrushchev’s “thaw” weakened the oppression of totalitarianism, Stalin’s personality cult was exposed, and the idea of ​​prevention was revived in the field of criminal policy. N. Khrushchev spoke in favor of the crime prevention criterion at the 20th Congress of the CPSU (1956), and then repeated this at the 21st Congress (1959). “It is necessary to take measures that would prevent, and then completely eliminate, the occurrence of any actions by individuals that are harmful to society. The main thing is prevention and educational work" At the XXI Congress (1961), a new Program of the CPSU was adopted, according to which the main attention in criminal policy “should be aimed at preventing crimes.” Khrushchev saw prevention as a panacea for deviant manifestations. Therefore, this period was characterized by the massive transfer of accused persons to bail, and convicts to “re-education to the labor collective.”

It must be said that the “breath of freedom” during the “thaw” had a positive effect on the social climate. Crime rate has dropped to its lowest level in years Soviet power(1963 - 397.7, 1964 - 392.2, 1965 - 388.7 per 100,000 thousand). Another important social indicator - the suicide rate also turned out to be relatively low: 17.1 in 1965, while already in 1970 - 23.1 and then a constant increase until Gorbachev's perestroika (in 1984 - 29.7 in the USSR and 38. 7 in the RSFSR with a subsequent decrease during the years of perestroika). The death rate (per 1,000 people) fell below 10 for the first time since 1955 and continued to decline until 1964.

The period from L. Brezhnev to M. Gorbachev is characterized by the ongoing collapse of the socialist economy, the agony of the regime, accompanied by an unprecedented increase in the number of anti-Soviet jokes. It was necessary to urgently introduce into the criminal code (Decree of the Presidium Supreme Council RSFSR dated 09/16/1966 with a subsequent addition dated 12/3/1982) “anecdotal” article 190-I: “Dissemination of deliberately false fabrications discrediting the Soviet state and social order" (Punished up to 3 years in prison).

Gorbachev’s “perestroika” was objectively one of the most radical attempts to save the dying system. He managed what seemed impossible to eliminate the dominance of one party, establish freedom of speech and press, ensure the holding of free elections, establish private property and free enterprise, destroy the Iron Curtain, and ensure freedom of movement, including abroad. Punitive practices have softened somewhat. If in 1985 45.2% of convicts were sentenced to imprisonment, then in 1986 - 37.7%, in 1987 - 33.7%, in 1988 - 34.1% with a subsequent increase. It is very significant that even short-term attempts to liberalize a totalitarian regime lead to favorable social consequences. This is hardly an accident, because the dynamics of some deviations in other countries of the former “socialist camp” express the same trends.

The “perestroika” of the political regime in the direction of liberalization ended after Russia switched to radical, abrupt changes. Today, sociologists speak with alarm about the criminalization of Russian society. The social reasons influencing this process include: crisis and collapse of values ​​and social norms; anomie; marginalization of society; widespread occurrence of delinquent subcultures; weakening of institutions of social control; growth of corruption in the state apparatus of power. IN Lately The government declares its commitment to liberal democratic values. But at the same time, the political regime continues to tighten. It is accompanied, unfortunately, by a retreat from liberalization of economic, social and especially political relations(construction of the “vertical of power”, the actual appointment of elected officials, political and economic pressure on opposition means mass media etc.).

In a reformed society, where some norms have been destroyed and others have not been created, the problem of forming, interpreting and applying norms becomes an extremely difficult matter. By destroying the norms formed in Soviet time, we are feverishly trying to create norms for the current stage of our development, turning our gaze either to the West or to the pre-revolutionary past.

The deviance of society and deviant behavior were, are and will be as long as society exists.

Social control, as a mechanism of self-organization of society, was, is and will be as long as society exists.

Social control or any other mechanism of self-preservation of society will never be able to “liquidate”, “overcome”, “overcome” deviance in general and any of its manifestations.

The modern world provides humanity with unprecedented opportunities, but also poses incredibly complex problems.

On the one hand: the globalization of economics, politics, culture, modern means of communication, the global information network, the experience of integration, the achievements of science, technology, and medicine could serve as the basis for the peaceful creative life of millions of people. On the other hand, political and religious extremism, international terrorism, interethnic bloody conflicts, the ambitions of dictators and the powerlessness of peoples, the growing gap between the countries of the “golden billion” and the rest of the world.

Undoubtedly, most societies are able to assimilate a considerable number of deviations from the norm without serious consequences for themselves, but persistent and widespread deviations can disrupt the organized life of society or even undermine it.

In this regard, it seems to us that the survival of both individual societies and humanity as a whole is possible provided:

  1. liberalization and democratization of political regimes;
  2. renunciation of political extremism and forceful methods of resolving interstate and internal conflicts;
  3. maximum tolerance towards dissent and other actions, towards minorities, other cultures and subcultures;
  4. real embodiment in external and domestic policy states of the principles of personal inviolability and protection of its rights and freedoms, the absolute value of every life and non-violence.

BIBLIOGRAPHY:

  1. Durkheim E. Method of Sociology. On the division of social labor. M., 1991.
  2. Parsons T. “General theoretical problems of sociology” in the book “Sociology Today”, M., 1965.
  3. Fromm Z. Anatomy human destructiveness. "Social sciences and modernity." 1992 No. 3.
  4. Yadov V.A. Sociological research: methodology, program, methods. M., 1997.

The work was presented at the scientific conference “Problems of international integration of national educational standards", April 23-27, 2007, Paris-London. Received by the editor on March 19, 2007.

Bibliographic link

Cherkesov B.A. SOCIAL NORMS AND DEVIANT BEHAVIOR // Basic Research. – 2007. – No. 9. – P. 112-116;
URL: http://fundamental-research.ru/ru/article/view?id=3668 (access date: 07/14/2019). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"

The existence of a person outside of society is impossible. In the course of his life, a person constantly enters into social interaction with other members of society. Human behavior is regulated by social norms that have developed as a result of historical development.

Concept of social norms

Social norms are clearly defined rules of behavior that govern a person’s relationship with society. Social norms play the role of the main restraining factor that does not allow a person to violate other people's interests in order to satisfy personal needs.

All modern social norms originate from spiritual norms characteristic of religious dogma. Many of them have been changed and modernized to meet the needs of modern society.

Diversity of social norms

As a rule, all social norms are closely interrelated with each other. At the moment, the following types of social norms exist:

Legal norms (rules of human behavior that are enshrined in relevant regulations);

Religious norms (standards of behavior that are enshrined in religious scriptures);

Moral norms (rules of behavior that are dictated by society to a person).

Deviant behavior: causes and prevention

Deviant behavior is human behavior that deviates from social norms.

The cause of deviant behavior can be factors such as insufficient knowledge of social norms, inability to perceive social norms due to gaps in education, illness (alcoholism, drug addiction).

The main preventive method of deviant behavior is educational work with children at school and at home. Providing medical and psychological assistance to people who suffer from alcoholism and drug addiction.

Social control and self-control

Social control is the control of society over a person, which is carried out with the aim of preventing him from committing an unlawful act.

Self-control is a person’s independent control of his own actions and their correlation with existing social norms.

Thus, the circumference ( C) can be calculated by multiplying the constant π per diameter ( D), or multiplying π by twice the radius, since the diameter is equal to two radii. Hence, circumference formula will look like this:

C = πD = 2πR

Where C - circumference, π - constant, D- circle diameter, R- radius of the circle.

Since a circle is the boundary of a circle, the circumference of a circle can also be called the length of a circle or the perimeter of a circle.

Circumference problems

Task 1. Find the circumference of a circle if its diameter is 5 cm.

Since the circumference is equal to π multiplied by the diameter, then the length of a circle with a diameter of 5 cm will be equal to:

C≈ 3.14 5 = 15.7 (cm)

Task 2. Find the length of a circle whose radius is 3.5 m.

First, find the diameter of the circle by multiplying the length of the radius by 2:

D= 3.5 2 = 7 (m)

Now let's find the circumference by multiplying π per diameter:

C≈ 3.14 7 = 21.98 (m)

Task 3. Find the radius of a circle whose length is 7.85 m.

To find the radius of a circle based on its length, you need to divide the circumference by 2 π

Area of ​​a circle

The area of ​​a circle is equal to the product of the number π per square radius. Formula for finding the area of ​​a circle:

S = πr 2

Where S is the area of ​​the circle, and r- radius of the circle.

Since the diameter of a circle is equal to twice the radius, the radius is equal to the diameter divided by 2:

Problems involving the area of ​​a circle

Task 1. Find the area of ​​a circle if its radius is 2 cm.

Since the area of ​​a circle is π multiplied by the radius squared, then the area of ​​a circle with a radius of 2 cm will be equal to:

S≈ 3.14 2 2 = 3.14 4 = 12.56 (cm 2)

Task 2. Find the area of ​​a circle if its diameter is 7 cm.

First, find the radius of the circle by dividing its diameter by 2:

7:2=3.5(cm)

Now let's calculate the area of ​​the circle using the formula:

S = πr 2 ≈ 3.14 3.5 2 = 3.14 12.25 = 38.465 (cm 2)

This problem can be solved in another way. Instead of finding the radius first, you can use the formula for finding the area of ​​a circle using the diameter:

S = π D 2 ≈ 3,14 7 2 = 3,14 49 = 153,86 = 38.465 (cm 2)
4 4 4 4

Task 3. Find the radius of the circle if its area is 12.56 m2.

To find the radius of a circle by its area, you need to divide the area of ​​the circle π , and then extract from the obtained result Square root:

r = √S : π

therefore the radius will be equal to:

r≈ √12.56: 3.14 = √4 = 2 (m)

Number π

The circumference of objects surrounding us can be measured using a measuring tape or rope (thread), the length of which can then be measured separately. But in some cases, measuring the circumference is difficult or practically impossible, for example, the inner circumference of a bottle or simply the circumference of a circle drawn on paper. In such cases, you can calculate the circumference of a circle if you know the length of its diameter or radius.

To understand how this can be done, let’s take several round objects whose circumference and diameter can be measured. Let's calculate the ratio of length to diameter, and as a result we get the following series of numbers:

From this we can conclude that the ratio of the length of a circle to its diameter is a constant value for each individual circle and for all circles as a whole. This relationship is denoted by the letter π .

Using this knowledge, you can use the radius or diameter of a circle to find its length. For example, to calculate the length of a circle with a radius of 3 cm, you need to multiply the radius by 2 (this is how we get the diameter), and multiply the resulting diameter by π . As a result, using the number π We learned that the length of a circle with a radius of 3 cm is 18.84 cm.

The circumference of a circle is indicated by the letter C and is calculated by the formula:

C = 2πR,
Where R - radius of the circle.

Derivation of the formula expressing the circumference

Path C and C’ are the lengths of circles of radii R and R’. Let us inscribe a regular n-gon into each of them and denote their perimeters by P n and P" n, and their sides by a n and a" n. Using the formula for calculating the side of a regular n-gon a n = 2R sin (180°/n) we get:
P n = n a n = n 2R sin (180°/n),
P" n = n a" n = n 2R" sin (180°/n).
Hence,
P n / P" n = 2R / 2R". (1)
This equality is valid for any value of n. We will now increase the number n without limit. Since P n → C, P" n → C", n → ∞, then the limit of the ratio P n / P" n is equal to C / C". On the other hand, by virtue of equality (1), this limit is equal to 2R/2R". Thus, C/C" = 2R/2R". From this equality it follows that C/2R = C"/2R", i.e. . The ratio of the circumference of a circle to its diameter is the same number for all circles. This number is usually denoted by the Greek letter π (“pi”).
From the equality C / 2R = π we obtain the formula for calculating the circumference of a circle of radius R:
С = 2πR.

Circular arc length

Since the length of the entire circle is 2πR, then the length l of an arc of 1° is equal to 2πR / 360 = πR / 180.
That's why length l of an arc of a circle with degree measure α expressed by the formula
l = (πR / 180) α.

A circle consists of many points that are at equal distances from the center. It's flat geometric figure, and finding its length is not difficult. A person encounters a circle and a circle every day, regardless of what field he works in. Many vegetables and fruits, devices and mechanisms, dishes and furniture are round in shape. A circle is the set of points that lies within the boundaries of the circle. Therefore, the length of the figure is equal to the perimeter of the circle.

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Characteristics of the figure

In addition to the fact that the description of the concept of a circle is quite simple, its characteristics are also easy to understand. With their help you can calculate its length. The inner part of the circle consists of many points, among which two - A and B - can be seen at right angles. This segment is called the diameter, it consists of two radii.

Within the circle there are points X such, which does not change and is not equal to unity, the ratio AX/BX. In a circle, this condition must be met; otherwise, this figure does not have the shape of a circle. Each point that makes up a figure is subject to the following rule: the sum of the squared distances from these points to the other two always exceeds half the length of the segment between them.

Basic circle terms

In order to be able to find the length of a figure, you need to know the basic terms relating to it. The main parameters of the figure are diameter, radius and chord. The radius is the segment connecting the center of the circle with any point on its curve. The magnitude of a chord is equal to the distance between two points on the curve of the figure. Diameter - distance between points, passing through the center of the figure.

Basic formulas for calculations

The parameters are used in the formulas for calculating the dimensions of a circle:

Diameter in calculation formulas

In economics and mathematics there is often a need to find the circumference of a circle. But also in Everyday life you may encounter this need, for example, when building a fence around a swimming pool round shape. How to calculate the circumference of a circle by diameter? In this case, use the formula C = π*D, where C is the desired value, D is the diameter.

For example, the width of the pool is 30 meters, and the fence posts are planned to be placed at a distance of ten meters from it. In this case, the formula for calculating the diameter is: 30+10*2 = 50 meters. The required value (in this example, the length of the fence): 3.14*50 = 157 meters. If the fence posts stand at a distance of three meters from each other, then a total of 52 of them will be needed.

Radius calculations

How to calculate the circumference of a circle from a known radius? To do this, use the formula C = 2*π*r, where C is the length, r is the radius. The radius in a circle is half the diameter, and this rule can be useful in everyday life. For example, in the case of preparing a pie in a sliding form.

To prevent the culinary product from getting dirty, it is necessary to use a decorative wrapper. How to cut a paper circle of the appropriate size?

Those who are a little familiar with mathematics understand that in this case you need to multiply the number π by twice the radius of the shape used. For example, the diameter of the shape is 20 centimeters, respectively, its radius is 10 centimeters. According to these parameters there is required size circle: 2*10*3, 14 = 62.8 centimeters.

Handy calculation methods

If it is not possible to find the circumference using the formula, then you should use available methods for calculating this value:

  • If a round object is small, its length can be found using a rope wrapped around it once.
  • The size of a large object is measured as follows: a rope is laid out on a flat surface, and a circle is rolled along it once.
  • Modern students and schoolchildren use calculators for calculations. Online, you can find out unknown quantities using known parameters.

Round objects in the history of human life

The first round-shaped product that man invented was the wheel. The first structures were small round logs mounted on an axle. Then came wheels made of wooden spokes and rims. Gradually, metal parts were added to the product to reduce wear. It was in order to find out the length of the metal strips for the wheel upholstery that scientists of past centuries were looking for a formula for calculating this value.

A pottery wheel has the shape of a wheel, most parts in complex mechanisms, designs of water mills and spinning wheels. Round objects are often found in construction - frames of round windows in Romanesque architectural style, portholes in ships. Architects, engineers, scientists, mechanics and designers every day in their field professional activity are faced with the need to calculate the size of a circle.