Zinaida Trubina
Research work “Riddles of balloons”
MUNICIPAL PRE-SCHOOL EDUCATIONAL INSTITUTION
KINDERGARTEN No. 24 MUNICIPAL EDUCATION
UST-LABINSKY DISTRICT.
Research paper topic:
« Balloon Riddles.»
Completed
Menafov Shamil
Syrovatkina Victoria.
Educator
Trubina Zinaida Viktorovna.
INTRODUCTION…3
HISTORY OF CREATION BALLOONS…. 4
PRACTICAL PART…7
CONCLUSION…. 11
BIBLIOGRAPHY…. 12
APPLICATIONS…. 13
INTRODUCTION
Balloons. It seems like such a simple and ordinary thing. But in fact, this is a huge scope for physical experiments. You can use them to perform various tests and experiments.
Project objectives
1. Conduct a series of experiments and tests on balls
2. Analyze the observed phenomena and formulate conclusions
Create a multimedia presentation
.Target: make a selection of experiments in physics that can be shown on balloons.
Tasks: 1. Review of literature and the Internet to find experiments on balloons.
2. Check whether all experiments are feasible and adjust the progress of the experiments. Carry out these experiments.
3. Explain the result of the experiment
Methods research:
1. Study of literature.
2. Search the Internet.
3. Conducting experiments.
4. Observation.
A little history.
Looking at modern balloons, many people think that this bright, cuddly toy has only recently become available. Some more knowledgeable people believe that air balls appeared somewhere in the middle of the last century.
But in fact - no! Story balls, filled air, started much earlier. In former times, painted balls made from animal intestines decorated the squares where sacrifices and festivities of noble people of the Roman Empire were held. After air Balloons began to be used by traveling artists, creating decorations with balloons to attract new viewers. Subject balloons also touched upon in Russian chronicles - buffoons, performing for Prince Vladimir, used balls made from bull bladders.
The first balls of the modern type were created by the famous English electricity researcher, Queen's University Professor Michael Faraday. But he did not create them to distribute to children or to sell at a fair. He was just experimenting with hydrogen.
Interesting is the way Faraday created his balloons. He cut out two pieces of rubber, placed them on top of each other, glued the outline together, and sprinkled flour in the middle so that the sides did not stick to each other.
Faraday's idea was taken up by rubber toy pioneer Thomas Hancock. He created his balls in the form of a set "do it yourself" consisting of a bottle of liquid rubber and a syringe. In 1847, vulcanized balls were introduced in London by J. G. Ingram. Even then, he used them as toys to sell to children. As a matter of fact, it is they who can be called the prototype of modern balls.
About 80 years later, the scientific hydrogen bag turned into a popular fun: Rubber balls were widely used in Europe during city festivals. Due to the gas that filled them, they could rise upward - and this was very popular with the public, who had not yet been spoiled by any air flights, nor other miracles of technology.
In 1931, Neil Tylotson produced the first modern, latex balloon. And since then air The balls were finally able to change! Before that, they could only be round - but with the advent of latex, for the first time it became possible to create long, narrow balls.
This innovation immediately found application: designers who decorate holidays began to create from balls compositions in the form of dogs, giraffes, airplanes, hats. Clowns began to use them, inventing unusual figures.
PRACTICAL PART
Experiment No. 1
1. Ball piercing trick.
EquipmentYou will need an inflated balloon, tape, metal knitting needle or long awl.
It is necessary to stick pieces of tape on diametrically opposite points of the ball. It will be better if these points are close to the “poles” (i.e. the top and the very bottom). Then the trick can work even without tape. Feel free to insert an awl or knitting needle so that it passes through the areas sealed with tape.
The secret of the trick is that although a hole will form, the tape will prevent the pressure from breaking the ball. And the knitting needle itself will close the hole, preventing air to come out of it.
Experiment No. 2
"2. Fireproof ball trick.
Equipment candle, one inflated and one new balloon(this second balloon must be filled with tap water, and then inflated and tied so that the water remains inside).
Light a candle, bring a regular ball to the fire - as soon as the flame touches it. it will burst.
Now let’s “conjure” the second ball and declare that it is no longer afraid of fire. Bring it to the candle flame. The fire will touch the ball, but nothing will happen to it!
This trick clearly demonstrates such a physical concept as “thermal conductivity”.
The secret of the trick is that the water in the ball “takes” all the heat from the candle onto itself, so the surface of the ball does not heat up to a dangerous temperature.
Experiment No. 4
Air ball as a jet engine.
Equipment ball, machine.
This visual model demonstrates the principle work jet engines. Its principle work in that that jet air, escaping from the ball, after it has been inflated and released, pushes the machine in the opposite direction.
Experiment No. 5
Inflate the balloon with carbon dioxide.
Equipment: plastic bottle, ball, vinegar, soda, funnel.
Pour baking soda into a plastic bottle through a funnel. (we poured 2 tablespoons) and pour a little table vinegar there (by eye). Many people are familiar with this experience: this is how children are usually shown a volcano - as a result of a violent chemical reaction, a lot of foam is produced, which “escaps” from the vessel. But this time we are not interested in foam (this is just an appearance, but what is produced during this reaction is carbon dioxide. It is invisible. But we can catch it if we immediately pull it onto the neck of the bottle balloon. Then you can see how the released carbon dioxide inflates the balloon.
The secret of the trick: Add vinegar to the soda - as a result of a chemical reaction, carbon dioxide is released, which inflates the balloon.
Experiment No.6
Trick with inflating a balloon in a bottle.
Equipment Prepare two plastic bottles and two uninflated hot air balloon. Everything should be the same, except that in one bottle you need to make an inconspicuous small hole in the bottom. Pull the balls onto the necks of the bottles and tuck them inside. Make sure you get a bottle with a hole. Offer to arrange competition: Who will be the first to inflate the balloon inside the bottle? The result of this competition is a foregone conclusion - your partner will not be able to inflate the balloon even a little, but you will succeed in doing it perfectly.
The secret of the trick is that in order to inflate a ball in a bottle, you will need a place where it will expand. But the whole bottle is already full air! Therefore, there is nowhere for the ball to inflate. To make this happen, you need to make a hole in the bottle through which excess air.
Experiment No.7
Losing weight and getting fat ball.
Equipment: ball, tailor's meter, refrigerator.
The fact that various bodies and gases expand from heat and contract from cold can be easily demonstrated by example hot air balloon.
The experiment can be carried out using a refrigerator. Let's inflate in a warm room balloon. Using a tailor's meter, measure its circumference (we got 80.6 cm). After this, put the ball in the refrigerator for 20-30 minutes. And again we measure its circumference. We found that the ball “lost weight” by almost a centimeter (in our experience it became 79.7 cm). This happened due to the fact that air inside the ball it shrank and began to occupy less volume.
Experiment No.8
Lunokhod on air cushion
Equipment to make a lunar rover for us will be needed: CD, glue, bottle cap with baby water, balloon.
Before our balloons burst, we decided to use them to create vehicles. Lunokhod on air pillow The lid was glued to the disk, a balloon was put on top and it was inflated. There was an attempt to first inflate the balloon and then put it on the cork, but this turned out to be very inconvenient. Air breaks out of the ball and is created "layer" between the floor and the disk - airbag.
CONCLUSION
On air balls, you can study the laws of pressure of bodies and gases, thermal expansion (compression, gas pressure, density of liquids and gases, Archimedes' law; you can even design instruments for measuring and research physical processes.
Our experiments prove that the ball is an excellent tool for studying physical phenomena and laws. Use our you can work at school, in 7th grade, when studying sections "Initial information about the structure of matter", "Pressure of solids, liquids and gases". The collected historical material can be used in physics classes and extracurricular activities.
A computer presentation created on the basis of the practical part will help schoolchildren quickly understand the essence of the physical phenomena being studied and will arouse a great desire to conduct experiments using simple equipment
It is obvious that our Job contributes to the formation of genuine interest in the study of physics.
While studying this topic, we found information about what to inflate air Balloons are not only fun, but also useful! It turns out that they “give” health to our lungs. Inflation balls has a positive effect on our throat (it even serves as a means of preventing sore throat, and also helps strengthen our voice. Singers often use this help, since such training helps them breathe correctly while singing.
Bibliography
1. The Big Book of Experiments for Schoolchildren / ed. A. Meyani - M.: Rosmen Press. 2012
2. http://adalin.mospsy.ru/l_01_00/op09.shtml
3. http://class-fizika.narod.ru/o54.htm
4http://physik.ucoz.ru/publ/opyty_po_fizike/ehlektricheskie_javlenija
5. Electronic resource]. Mode access: www.demaholding.ru
6. [Electronic resource]. Mode access: www.genon.ru
7. [Electronic resource]. Mode access: www.brav-o.ru
8. [Electronic resource]. Mode access: www.vashprazdnik.com
9. [Electronic resource]. Mode access: www.aerostat.biz
10. [Electronic resource]. Mode access: www.sims.ru
11. Turkina G. Physics on balloons. // Physics. 2008. No. 16.
“Volume of a ball” - Find the volume of the cut off spherical segment. A ball is inscribed in a cone whose base radius is 1 and its generatrix is 2. Find the volume of a sphere inscribed in a cylinder whose base radius is 1. Volume of a torus. Find the volume of a sphere inscribed in a cube with edge equal to one. Exercise 22. Find the volume of a ball whose diameter is 4 cm.
“Circle circle sphere ball” - Ball and sphere. Ball. Circle. Area of a circle. Diameter. Remember how a circle is defined. You are required to be attentive, focused, active, and precise. Geometric pattern. Center of the ball (sphere). Try to define a sphere using the concepts of distance between points. Computer center.
“Sphere and ball” - Three points are given on the surface of the ball. Problem on the theme ball (d/z). Section of a sphere by a plane. Any section of a ball by a plane is a circle. Tangent plane to a sphere. This point is called the center of the sphere, and this distance is called the radius of the sphere. The tale of the emergence of the ball. The section passing through the center of the ball is a large circle. (diametrical section).
“Balloon” - Since ancient times, people have dreamed of the opportunity to fly above the clouds and swim in the ocean of air. Airships are equipped with low-power and economical diesel engines. It is much easier to lift and lower a ball filled with hot air. Speed 120-150 km/h. Airships. Aeronautics. It is difficult to imagine the modern world without advertising, and here balloons have been used.
“Cylinder cone ball” - Volume of the spherical sector. Find the volume and surface area of the sphere. Definition of a ball. Problem No. 3. Surface areas of bodies of rotation. Ball sector. The section of a ball by the diametrical plane is called a great circle. Bodies of rotation. The cross section of a cylinder with a plane parallel to the bases is a circle.
“Scientific and practical conference” - M.V. Lomonosov 2003. The focus of Russian education... From the history of the school scientific and practical conference. About how many wonderful discoveries the spirit of enlightenment is preparing for us... The sixth school scientific and practical conference dedicated to Khuzangay 2007. The second school scientific and practical conference dedicated to the 290th anniversary.
Slide 1
BALL Multimedia textbook on stereometry for 11th grade mathematics teacher of Municipal Educational Institution “Secondary School No. 15” in Bratsk Anikina A.I.Slide 2
R O A sphere is a surface consisting of all points in space located at a given distance from a given point. This point is called the center of the sphere. This distance is the radius of the sphere. A segment connecting two points of the sphere and passing through its center is called the diameter of the sphere.
Slide 3
The sphere is obtained by rotating the semicircle ACB around the diameter AB. A C B A body bounded by a sphere is called a ball. The center, radius and diameter of the sphere are also called the center, radius and diameter of the ball.
Slide 4
R M(x;y;z) C(x0;y0;z0) z y x O Sphere equation An equation with three unknowns x, y and z is called a surface equation F MC = If point M lies on a given sphere, then MC = R or MC2 = R2, i.e. the coordinates of point M satisfy the equation (x – x0)2+(y – y0)2+(z – z0)2 =R2 If point M does not lie on the given sphere, then MC2 ≠ R2, i.e. the coordinates of point M do not satisfy the equation. Therefore, in a rectangular coordinate system, the equation of a sphere of radius R with center C(x0;y0;z0) has the form (x – x0)2+(y – y0)2+(z – z0)2 =R2
Slide 5
RELATIVE POSITION OF SPHERE AND PLANE α y x z C (0;0;d) O R 1 d< R . Тогда R2- d2 >0 r = If the distance from the center of the sphere to the plane is less than the radius of the sphere, then the section of the sphere by the plane is a circle d
Slide 6
α R O The section of a ball by a plane is a circle. If the cutting plane passes through the center of the ball, then d = 0 and the section produces a circle of radius R, i.e. a circle whose radius is equal to the radius of the ball. This circle is called the great circle of the ball
Slide 7
O d C (0;0;d) α y x z d = R Then R2 – d2 =0 Therefore, point O is the only common point of the sphere and the plane. If the distance from the center of the sphere to the plane is equal to the radius of the sphere, then the sphere and the plane have only one common point. 2
Slide 8
α y x d z C (0;0;d) O 3 d > R Then R2 – d2< 0 , и уравнению не удовлетворяют координаты никакой точки. Если расстояние от центра сферы до плоскости больше радиуса сферы, то сфера и плоскость не имеют общих точек.
Slide 9
α O A Tangent plane to a sphere A plane that has only one common point with the sphere is called the tangent plane of the sphere. Their common point is called the tangency point of the plane and the sphere. Theorem 1: The radius of a sphere drawn to the point of contact between the sphere and the plane is perpendicular to the tangent plane. Theorem 2: If the radius of a sphere is perpendicular to the plane passing through its end lying on the sphere, then this plane is tangent to the sphere.
Slide 10
For the area of a sphere, we take the limit of the sequence of surface areas of polyhedra described around the sphere as the largest size of each face tends to zero. We obtain a formula for calculating the area of a sphere of radius R: S = 4 π R2
Slide 11
Slide 12
Slide 13
Slide 14
B O R r x M A x WITH THE VOLUME OF THE BALL Consider a ball of radius R and center at point O and choose the Ox axis in an arbitrary way. The section of the ball by a plane perpendicular to the Ox axis and passing through point M on this axis is a circle with center at point M. From a right triangle We find the OMC. Using the basic formula for calculating volumes, we obtain Since S(x) = πr2, then S(x) = π (R2 - x2)
main idea
Over the centuries, humanity has not ceased to expand its scientific knowledge in one or another field of science. Many scientific geometers, and even ordinary people, were interested in such a figure as ball and its “shell”, called sphere. Many real objects in physics, astronomy, biology and other natural sciences are spherical. Therefore, the study of the properties of the ball was given a significant role in various historical eras and is given a significant role in our time.
- Establish connections between geometry and other fields of science.
- To develop the creative activity of students, the ability to independently draw conclusions based on the data obtained as a result of research.
- Develop students' cognitive activity.
- Foster a desire for self-education and improvement.
Working groups and research questions
Group “Mathematics”
- Summarize the material on the topic “Sphere and Ball” studied in the school geometry course.
- Find and compare all definitions of sphere and sphere.
- Prepare summary tables and a collection of tasks.
Group “Geographers”
- Find the first mentions of the Earth as a spherical surface.
- Find materials indicating the evolutionary development of planet Earth.
Group “Astronomers”
- Find connections between geometry and astronomy.
- Find evidence of the sphericity of the Earth from the point of view of astronomy.
- Find materials about the structure of the solar system.
Group “Philosophers”
- Find material that connects the geometric body - the sphere - with the concepts of philosophy.
- Determine the types of spheres from the point of view of philosophy.
Group “Art Critics”
Find paintings and engravings that depict the sphere.
Group “Academic Council”
Summarize the lesson and evaluate the work of each group.
Reporting materials
- Summary posters.
- Drawings.
- Messages.
- Collection of problems.
- Presentation (in this article, graphic material from the presentation is used as illustrations).
Lesson type: generalization of knowledge gained in the geometry course about the sphere and ball.
Methods and techniques of work: implementation of design and research technologies.
Equipment:
- Textbook of geometry 10-11, authors L.S. Atanasyan, V.F. Butuzov and others.
- Slides, posters.
- Encyclopedic dictionaries.
- Sphere and ball models.
- Globe, map.
Teacher's opening speech
Dear guys! Today’s lesson is a general lesson on the topic “Sphere and Ball”, and it takes place within the framework of design and research technologies. In the lesson we will generalize knowledge about the sphere and ball, and also learn something new about these concepts from other fields of science. Not a single science has ignored these geometric concepts. Many real objects in astronomy, biology, chemistry and other natural sciences have the shape of a sphere and a ball. In various historical eras, the study of these concepts has been and continues to play a significant role.
The epigraph to our lesson will be the words of Wiener: “The highest purpose of geometry is precisely to find hidden order in the chaos that surrounds us.”
Today we will try to streamline the chaos reigning around the sphere and ball.
The following working groups took part in preparing the lesson:
– mathematicians;
– geographers;
– astronomers;
– philosophers;
– art critics.
Each group had its own range of research questions. The general summary of the lesson will be “academic advice”. As usual, in your notebooks you write down the studies that interest you and the conclusions of the groups.
So, let’s write down in the notebooks the date of the lesson, the topic of the lesson (dictate). Today in the lesson we must answer the question “A ball and a sphere - are they ordinary geometric concepts or something more?”
Let's give the floor to a group of mathematicians.
“Mathematicians”
1st student. Our group once again carefully studied the material about the ball and sphere, and then generalized it (a brief summary of the material from the textbook “Geometry 10-11” is considered).
2nd student. We also know what the relative position of the sphere and the plane is. Let R be the radius of the sphere, d be the distance from the center of the sphere to the plane. (Drawings from the textbook about the relative position of a sphere and a plane are considered.)
In addition, when solving problems on the topic “Sphere and ball”, we find its surface area and volume.
and V=4/3?R 3, where R is the radius of the sphere.3rd student. Our group conducted research on all the definitions of sphere and ball that were found in the mathematical encyclopedic dictionary, in the Great Encyclopedic Dictionary, in the Brockhaus and Efron encyclopedia, in the old geometry textbook by the author Kiselev, published in 1907. And we came to the conclusion that the definitions of a ball and a sphere have undergone virtually no changes over time. For example, in the mathematical encyclopedic dictionary ball is a geometric body obtained by rotating a circle around its diameter; a ball is a set of points whose distance from a fixed point O (center) does not exceed a given R (radius).
The Big Encyclopedic Dictionary gives a similar definition.
In the Brockhaus and Efron Encyclopedia ball – a geometric body bounded by a spherical or spherical surface. All points of the sphere are located at equal distances from the center. Distance is the radius of the ball.
In Kiselev’s geometry – a body resulting from the rotation of a semicircle around the diameter limiting it is called. a ball, and the surface formed by a semicircle is called. spherical or spherical surface. This surface is the locus of points equally distant from the same point, called the center of the ball.
Conclusion. So, as a result of the work done by our group, we came to the conclusion that for quite a long time the definitions of a sphere and a ball have not changed. We have prepared a collection of problems on the topic “Sphere and ball”, and we hope that these problems will help to apply theoretical knowledge about the sphere and ball in practice. To support our research, let's put theoretical knowledge into practice (students solve several problems).
Teacher's word
Thanks to the group of mathematicians who summarized the material about the sphere and the ball, and also prepared a collection of practical problems. You and I know that the shape of a ball is very common in nature and in the environment around us. The most interesting object with a spherical surface is our planet Earth. Now a group of “geographers” will introduce us to their research. Please.
“Geographers”
1st student. The purpose of our work is to study what the Earth was like in the ideas of the ancients, and how the formation of the Earth as a spherical surface took place. While preparing for the lesson, we found a book, or rather, pages from a book, from which we can judge that it was an encyclopedia for children, published before the 1917 revolution; this can be seen from the font.
So, in this book it is written that “a very long time ago people thought that the earth was flat, like a table, and that if you walked straight and straight, you could reach the end of the earth. But then scientists appeared who proved that the earth is a huge ball with no end.”
There is a poem in this book:
I've been standing for hundreds and hundreds of years,
There is no end or edge for me.
I stand like a strong hero,
And cover my chest
Deserts, steppes, mountain ranges,
Forests, fields, meadows,
Villages, villages, cities,
The seas are icy water.
I give shelter here and there,
Animals, people and beasts.
I feed everyone and sing to everyone,
I send my grace to everyone.
I am like a huge round ball!
I am God's work, God's gift!
On the screen we see our land as it is depicted on geographical maps.
2nd student. Continuing our research, we learned that the ancients considered the Earth to be a flat disk surrounded on all sides by the ocean. However, already at that time people began to wonder why water always occupies the lowest places (this applies to seas and oceans); Why is there a gradual appearance or removal of tall objects as you approach or move away from them? While traveling around the world, sailors noticed that when returning to the same place, there was a loss or gain of an entire day, which would be completely impossible if the Earth had the shape of a disk.
So, evidence of the sphericity of the Earth at present is:
- Always a circular figure of the horizon in the ocean and in open lowlands or plateaus;
- Gradual approach or removal of objects;
- Traveling around the world.
3rd student. While studying various geographical maps, we discovered that in geography there are place names associated with the ball. For example, between the Northern and Southern islands of Novaya Zemlya there is a strait that connects the Barents and Kara seas, which is called Matochkin Shar, or a strait between the shores of Vaigach Island and the mainland of Eurasia - Yugorsky Shar. We think that these straits are called balls due to the fact that their size and bottom shape resemble a spherical surface.
Conclusion. Our group studied the Earth as a spherical surface. Of course, what we learned and shared with you is a small fraction of the enormous material about the Earth. We hope you are interested in our research and take the time to read something new.
A student from a group of mathematicians proposes to solve a problem to find the volume of a globe standing on a table.
Teacher's word
Thanks to the group of “geographers”.
However, the Earth is not just the surface on which we move, it is also a planet in the solar system. How the study of the sphericity of the Earth took place in the field of astronomy - our “astronomers” will tell us about this.
“Astronomers”
1st student. Our group studied the Earth from an astronomical point of view. In the course of our research, we learned that in ancient times people believed that the Earth was flat. According to their ideas, the sky was something like an inverted bowl, along which the Sun and stars moved. This is how the Babylonians saw the Earth and the sky (drawing on the screen). However, the movement of people from place to place forced them to look for some signs to choose the right direction. One such sign was the stars.
Thus, from the very beginning of human life, knowledge of the Earth was combined with the study of the sky.
The first impetus for changing views on the shape of the Earth was given by the practice of observing the sky, to which people were forced to turn. They noticed that when moving long distances, the appearance of the sky also changes: some stars cease to be visible, others, on the contrary, appear above the horizon. This speaks in favor of the sphericity of the Earth. Observations of lunar eclipses, during which the round edge of the earth's shadow is invariably visible on the lunar disk, proved that the Earth is spherical.
Lived in the 4th century BC. the greatest Greek scientist Aristotle developed and substantiated the doctrine of the sphericity of the Earth. He believed that all “heavy” bodies tend to approach the center of the world and, gathering around this center, form the globe.
While studying the Earth from an astronomical point of view, our group discovered in an astronomy textbook from the 1939 edition a map of the Earth, which was compiled by the Greek scientist Hecataeus in the 5th century BC. (map on screen). In the same textbook we found a map of the Earth in the Middle Ages - the era of the dominance of the Christian Church. On the map, north is on the left, south is on the right. It depicts the “sacred” Lands, Jerusalem and an imaginary sacred paradise.
2nd student. For the first time, the scientist astronomer Ptolemy tried to unite all the information about the Earth that then existed. According to his teaching, the Earth has the shape of a ball and remains motionless. She is at the center of the world and is the goal of creation. All other celestial bodies exist for the Earth and revolve around it. Ptolemy's theory was geometrically correct and served the practical purpose of pre-calculating the positions of the Sun and planets.
3rd student. Pay attention to the model of the solar system, which is located on the table. You and I see all the planets of our system. The question is: why in this model, as in many others, are all the planets of the solar system represented as spheres? The fact is that, under the influence of the forces of mutual attraction, their entire mass is concentrated in the center and takes the shape of a body whose surface is the smallest. And from geometry we know that of all bodies of rotation, the ball has the smallest surface.
By the way, stars also have the shape of a ball, or, more correctly, a spherical shape.
The volume and surface area of the planets of the solar system cannot be found without information from geometry. This is proven by the independent activity of the Pythagoreans in astronomy. Pythagoras himself taught that the Earth is spherical. The entire universe also has the shape of a ball, in the center of which the Earth freely rests on its own. The Earth's axis is also the axis around which the Sun, Moon and planets describe their paths without hindrance. These bodies must have a spherical shape, like the Earth. Because for Pythagoras the ball was perfect. Between the Earth and the sphere of the fixed stars these bodies are located in the following order: Moon, Sun, Mercury, Venus, Mars, Jupiter and Saturn. Their distances from the Earth are in certain harmonic relationships with each other, the consequence of which is the euphony produced by the combined movement of the luminaries, or the so-called music of the spheres.
Conclusion. Our group hopes that you were interested, and you, like us, noticed that none of the sciences can do without geometry. In conclusion, we would like to draw your attention to the screen where you see a photograph of the Earth from space.
Teacher's word
Thanks to a group of astronomers. The concept of a sphere, the term “sphere” is used not only in geometry, geography and astronomy. This term is also found in other fields of science. It’s not for nothing that we have a group of philosophers who will now share their research with us.
"Philosophers"
1st student. Walking in a shady grove, the Greek philosopher talked with his student. “Tell me,” asked the young man, “why are you overcome by doubts? You have lived a long life, are wise by experience and learned from the great Hellenes. How is it that so many unclear questions remain for you?”
In thought, the philosopher drew two circles in front of him with his staff: a small one and a large one. “Your knowledge is a small circle, and mine is a large one. But all that remains outside these circles is the unknown. A small circle has little contact with the unknown. The wider the circle of your knowledge, the greater its border with the unknown. And henceforth, the more you learn new things, the more unclear questions you will have.”
The Greek sage gave a comprehensive answer.
2nd student. Since our class is humanitarian, we decided to study the concept of sphere from a humanitarian point of view, namely, a philosophical one. Sphere is a general scientific concept that denotes the largest part of existence at any level: the universe, physical, chemical, biological, social and individual worlds.
In the social sciences, the concept of sphere has been used very widely and for a very long time. For example, there are 4 spheres of public life - economic, social, political and spiritual. The concept of sphere is one of the central and fundamental concepts of tetrasociology. It distinguishes: 4 spheres of social resources: people, information, organizations, things; 4 spheres of reproduction processes: production, distribution, exchange, consumption; 4 structural spheres of reproduction: social, informational, organizational, material; 4 spheres of states of social development: flourishing, slowing down, decline, death.
3rd student. There is a concept spheral democracy– a new form of democracy that arises in the information (global) society. The structural basis of spheral democracy are 4 spheres of social reproduction:
- sociosphere – its subject and product are people who are reproduced through humanitarian technologies of education, healthcare, etc.
- infosphere – its subject and product is information, which is reproduced by information technologies (both areas are directly related to us).
- orgsphere – its subject and product are social relations (political, legal, financial, managerial)
- technosphere – its subject and product are things that are reproduced by industrial and agricultural technologies.
4th student. There is also the concept spheral classes – these are 4 large productive groups of people covering the entire population.
- Socioclass – healthcare, education, social security workers and the non-working population - preschoolers, students, housewives, pensioners and the disabled.
- Infoclass – workers in the fields of science, culture, art, communications, information services.
- Organizational class – workers in the fields of management, finance, credit, insurance, defense, state security, customs, Ministry of Internal Affairs, etc.
- Technoclass – workers and peasants, workers in industries, agriculture and forestry, etc.
Spheral classes are inherent in the population of all countries of the world. Every person lives inside the so-called sphere. This is clearly presented on our table. All factors of the surrounding reality influence a person, and, consequently, the society in which he lives.
Conclusion. Everything we just talked about are the basic concepts of philosophy and sociology. We hope that these concepts will be useful to all of us in social studies lessons.
Teacher's word
Thanks philosophers. They introduced us to the concept of sphere from a philosophical point of view. I think this information is very important for all of us. And at the end of the lesson, we will give the floor to art critics.
“Art critics”
1st student. Our group also did not stand aside. We explored the work of the Dutch graphic artist Escher. His engravings are beautiful not only from an artistic point of view, but also no less beautiful from the point of view of geometry.
2nd student. Please look at the screen. You see the engravings: “Spirals on a sphere”, “Beech ball”, “Sphere with human figures”, “Three spheres”, “Concentric rings”. Aren't they beautiful? They contain the perfection of geometry, the so-called music of the spheres, which our astronomers spoke about. Escher's engravings contain the principle of symmetry, which can be more clearly seen on the sphere.
Teacher's word
Thanks to art critics. Now it's time to give the floor to our academic council.
Teacher's word
Thanks to the academic council. I think everyone agrees with him.
So, guys, today in the lesson we summarized the knowledge about the sphere and the ball, we learned a lot of new things. Returning to the epigraph of the lesson (read), we have brought a little order to the chaos that surrounds the sphere and ball.
Thanks to all groups. Your reporting material will be read and studied very carefully.
Homework: repeat everything about the sphere and the ball, prepare for the test work.
Thanks for the lesson. The lesson is over. Goodbye.
Nomination "The world around us"
There is hardly a single person who doesn’t love balloons! But I wondered - could this fun item also be useful? I wonder how does inflating balloons affect our health?
My hypothesis: Blowing up balloons is good for your health.
Project goal: Prove that blowing up balloons develops the respiratory system.
For this I:
- Conducted a survey in class
- I studied material on breathing in literature and on the Internet,
- I inflated balloons every day with the kids,
- took into account the frequency of exercises,
- performed introductory and final spirometry, as well as height measurements,
- processed the data and summed up the results,
- I tried to explain to my classmates the usefulness of such activities.
13 boys and 11 girls took part in the experiment. The balloons were inflated from Monday to Friday before the 1st lesson. Height and spirometry surveys were conducted in September and January.
To study this issue in more detail, I read in the literature about the structure and functions of the respiratory system, learned what vital capacity is, and that it consists of tidal volume, inspiratory reserve volume and expiratory reserve volume.
The experiment was carried out in grade 4 “B” at school No. 51.
After spirometry, we found out that on average, boys’ vital capacity is 28% below normal, and girls’ vital capacity is 18% below normal. This is explained by the fact that in the North people experience oxygen starvation, and also that Arkhangelsk is one of the cities with an unfavorable environmental situation. The VC of boys has a big difference with the required value. This is explained by the fact that girls have already entered a period of rapid growth, while this period begins later for boys.
So, I surveyed the kids about the respiratory system and conducted an experiment on using balloons in breathing exercises. She studied the structure and functions of the respiratory system from literary and Internet sources, analyzed the obtained spirometry data and compared them with the initial data.
Conclusion. We can say that breathing exercises using balloons increases vital capacity in girls by an average of 6% during the experiment, and by 2% in boys. The small increase can be explained by the fact that the experiment took little time. In general The hypothesis has been confirmed - inflating balloons is good for health.
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