Presentation on the topic of round bodies around us. Presentation on the topic: Round geometric bodies. Historical background about the sphere

04.04.2021

According to the definition adopted in 2006 by the International Astronomical Union, a planet is a body rotating around the Sun, massive enough to be spherical under the influence of its own gravity, in addition, it must have space near its orbit, free from other objects. If you pay attention to the first part of this formulation, then you can ask yourself a question - what is the minimum size of a body in general so that it has the shape of a ball?

It is believed that this figure is approximately 400 kilometers. At least in our solar system, at 397 km, Mimas is spherical, making it the smallest round body known.

Mimas

At the same time, this indicator depends on what the body consists of - therefore, for icy satellites it is less, for stone objects it is more. For example, the 530-kilometer asteroid Hygiea is definitely not round. The 420-kilometer Proteus (satellite of Neptune) is also not at all like Mimas.

Proteus

The infographic below shows all round bodies solar system having a diameter of less than 10 thousand kilometers. This includes both spherical objects and bodies like Haumea and Varuna, which are elliptical in shape. Also, for some reason, the already mentioned Hygiea and Proteus were recorded everywhere - but even with them, I think the picture is quite clear.

Another version of the infographic that only includes the bodies that have been visited spacecraft. Both pictures are good to use for a visual comparison in order to understand what a huge part of the solar system we have not yet studied.

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Slides captions:

Round bodies Presentation for a lesson in mathematics in the 6th grade Completed by Tremasova Tamara Nikolaevna MOU "SOSHp. Gorny Krasnopartizansky district of the Saratov region"

Cylinder - translated from Greek means "roller"

The surface of the cylinder consists of two bases and a side surface reamer

Sections of a cylinder by an inclined plane

Cylinder - formed by a rectangle rotating around one of the sides

The cone is translated from ancient Greek as "cone", "top".

The base of the cone is a circle. base

Cone sections - triangle, circle, ellipse.

Cone - formed by a right triangle rotating around one of the legs

Diameter A sphere, like a circle, has a center, a radius, and a diameter.

Sphere-surface of a ball (like a ball shell, orange peel)

When a sphere is cut by a plane, only a circle is obtained.

Ball - formed by a semicircle rotating around the diameter of the cut

Literature Literature and Internet resources Mathematics: Proc. for 5 cells. general education institutions /G.V. Dorofeev, S.B. Suvorova, E.A. Bunimovich and others; Ed. G.V. Dorofeeva, I.F. Sharygin. - 2nd ed., revised. - M.: Education, 2010. - 288 p.: ill. Mathematics: Proc. for 6 cells. general education Institutions / N.Ya. Vilenkin, V.I. Zhokhov, A.S. Chesnokov, S.I. Schwarzburd. – 6th ed. - M.: Mnemosyne, 2000. - 304 p.: ill. First steps in geometry. Sharygin I.F., Erganzhieva L.N. visual geometry. 5 - 6 cells: A manual for general educational institutions. – 3rd ed., stereotype. - M.: Bustard, 2000. - 192 p.: ill. http://uztest.ru/abstracts/?idabstract=970 472 http://vio.uchim.info/Vio_30/cd_site/articles/art_3_5.htm http://www.uchportal.ru/load/25-1- 0-25920

Thank you for your attention!

On the topic: methodological developments, presentations and notes

§one. COMBINATIONS OF THE BALL WITH POLYHEDRALS. THEOREM 1.1. Through any four points that do not belong to the same plane, one and only one can be drawn ...

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Cylinder Cone Sphere Historical Facts Interesting Authors

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Cylinder A cylinder is a body bounded by a cylindrical surface and two circles with borders. Lateral surface - cylindrical surface Base - circles Generators - Generators of a cylindrical surface Axis - straight line OO1 Radius - radius of the base Height - length of the generatrix

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Section types:

Axial If the cutting plane passes through the axis of the cylinder, then the section is a rectangle, two sides of which are generatrices, and the other two are the diameters of the bases of the cylinder Circular If the cutting plane is perpendicular to the axis of the cylinder, then the section is a circle. A cylinder can be obtained by rotating a rectangle around one of its sides

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Cylinder surface area

The total surface area of a cylinder is the sum of the areas of the lateral surface and the two bases. S=2πr(r+h) The area of the lateral surface of the cylinder is equal to the product of the circumference of the base and the height of the cylinder. The area of its development is taken as the area of the lateral surface of the cylinder. S=2prh

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Historical note about the cylinder

CYLINDER.. The word "cylinder" comes from the Greek kylindros, which means "roller", "skating rink".

Slide 7

Cone Cone - A body bounded by a conical surface and a circle with a boundary. Conical surface - lateral surface of the cone Base - circle Generators of the cone - generatrix of the conical surface Axis - straight line passing through the center of the base and the top of the cone

Slide 8

Section types:

Axial - If the cutting plane passes through the axis of the cone, then the section is an isosceles triangle. The base of which is the diameter of the base of the cone, and the sides are the generatrix of the cone Circular - If the cutting plane is perpendicular to the axis of the cone, then the section is a circle. The cone can be obtained by rotating a right triangle around one of the legs.

Slide 9

Cone surface area

The area of the full surface of the cone is called the sum of the areas of the lateral surface and the base S=πr(l+r) The area of the lateral surface of the cone is equal to the product of half the circumference of the base and the generatrix. S=πrl The area of its development is taken as the area of the lateral surface of the cone.

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Basic Formulas

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Historical background about the cone

CYLINDER.. The word "cylinder" comes from the Greek kylindros, which means "roller", "skating rink". CONE. The Latin word conus is borrowed from the Greek language (konos - plug, sleeve, pine cone). In the XI book of the "Beginnings" the following definition is given: if a right-angled triangle rotating around one of its legs returns to the same position from which it began to move, then the described figure will be a cone. Euclid considers only

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Sphere A sphere is a surface consisting of all points in space located at a given distance from a given point. A radius-segment connecting the center to any point of the sphere A diameter-segment connecting two points of the sphere and passing through its center. A chord is a segment that connects any two points on a sphere.

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Sphere area

For the area of the sphere, we take the limit of the sequence of areas of the surfaces of polyhedra circumscribed around the sphere as the largest size of each face tends to zero. S=4πR^2

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Tangent plane to sphere

A tangent plane to a sphere is a plane that has only one common point with the sphere. The point of contact is their common point. Theorem: The radius of the sphere, drawn to the point of contact between the sphere and the plane, is perpendicular to the tangent plane. Theorem: If the radius of a sphere is perpendicular to a plane passing through its end lying on the sphere, then this plane is tangent to the sphere

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Historical background about the sphere

However, both the words "ball" and "sphere" come from the same Greek word "sfire" - ball. At the same time, the word "ball" was formed from the transition of consonants sph into sh. In ancient times, the sphere was held in high esteem. Astronomical observations of the firmament invariably evoke the image of a sphere. The Pythagoreans taught about the existence of ten spheres of the Universe, along which celestial bodies allegedly move. They argued that the distances of these bodies from each other are proportional to the intervals of the musical scale. In this they saw the elements of world harmony. Pythagorean "music of the spheres" was contained in such semi-mystical reasoning. Aristotle believed that the spherical shape, as the most perfect, is characteristic of the Moon, the Sun, the Earth and all world bodies. Developing the views of Eudoxus, he believed that the Earth is surrounded by a series of concentric spheres. The sphere has always been widely used in various areas science and technology. In Book XI of the Elements, Euclid defines a sphere as a figure described by a semicircle rotating about a fixed diameter.

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Vodovzvodnaya Tower The Vodovzvodnaya Tower was built in 1488. The former name of the tower - Sviblova - is associated with the courtyard of the boyar Sviblova located nearby. In 1633, a water pump was installed in the tower to pump water into a reservoir located on the top of the tower. Through the pipes, water dispersed throughout the Kremlin. In 1805-1806, the tower was dismantled and rebuilt according to the project of the architect I.V. Egotov. In 1812, the tower was blown up by the French, and in 1819 it was restored under the leadership of O.I. Bove. The height of the tower to the star is 57.7 meters, with the star - 61.25 meters. The tower is a cylinder. The tower is round in cross section.

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Krivoarbatsky pereulok, building 10. Two huge white cylinders leaning against each other. Along the perimeter - sixty small diamond-shaped windows, creating the image of a beehive. On the facade there is a giant window several meters high. Above the window there is an inscription: "Konstantin Melnikov. Architect". The most famous (even iconic) building of the 1920s in Moscow. Konstantin Stepanovich Melnikov was born in Moscow in the family of a construction worker, a native of peasants, in 1890. After graduating from a parish school, he worked as a "boy" in a firm " Trading house Zalessky and Chaplin". Chaplin helped him enter the Moscow School of Painting, Sculpture and Architecture in 1905, and then, after graduating from Melnikov in 1913, the painting department advised him to continue his studies at the Architectural Department, which Konstantin Stepanovich graduated in 1917. At the senior courses of the School and in the first years after his graduation, Melnikov worked in the spirit of neoclassicism. However, already in the early 1920s, Konstantin Stepanovich sharply broke with various kinds of traditionalist stylizations. The very fact of the wide implementation of his works makes us take a different attitude towards those of his works that remained in projects and which in the 20s, in the sharp controversy of that period, were often declared "fantastic". In Melnikov's projects, the degree of uninhibited creative imagination of the master in matters of shaping is striking. It can be said with full confidence that in the 20th century there was no other architect who created there would be so many fundamentally new projects and such a level of novelty that their originality not only severely separated them from the works of other masters, but also distinguished them just as strongly from the works of their author himself.

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slide 1

ROUND BODIES / press conference / CYLINDER CONE BALL Presentation for a geometry lesson in grade 11.

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Generalization and deepening of knowledge about round bodies; their application (round bodies) in practice in everyday life; Development of logical thinking, creative activity, speech; Education of independence, activity, culture of communication. LESSON OBJECTIVES

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BALL, SPHERE I am a globe, an orange and a ball. I - round ball, I'm even a teapot.

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CONE You will find me easily in a funnel, On a Christmas tree, in a hat near a mushroom. Yes, the cone does not stand aside, Carrot is also me.

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TRUNCATED CONE Factory chimney and illuminated beacon - This cone is not at all simple - truncated!

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Here is a task not for the timid: Pack the ball in a box. It must fit tightly, so as not to shake it on the way.

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And in the end? Look: the cube is a box, the ball is inside.

Slide 9

Geometry: Proc. for 10-11 grades of secondary school / L.S. Atanasyan, V.F. Butuzov, S.B. Kadomtsev and others - M .: Education. 2007 Microsoft Office power point/collection of pictures/ http://iskystvo.ru/2008/10/ Used literature and Internet resources:

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Abstract

2. Educational institution.

3. Geometry, grade 11

5. Lesson topic. " Cylinder, cone, ball » /PRESS CONFERENCE/

Bibliography.

http://www.salda.ru/dishes/profi/

http://www.cook.freecopy.su/cookbook/?l=23&w=4306

http://www.srbp.ru/offers/20/805/2456.html

http://fotki.yandex.ru/users/mamuka532/view/60544/

http://arsel.flamber.ru/photos/1200076904/

http://www.vikar-plastic.com.ua/index.php?categoryID=301

http://yogaclassic.ru/post/2343

http://fantasyflash.ru/anime/index.php?kont=sea&n=3

http://fantasyflash.ru/anime/index.php?kont=disney&n=1

http://www.liveinternet.ru/photo/ha8xa7/post15454746/

http://s99-omsk.narod.ru/projects/v/mozaika.htm

http://iskystvo.ru/metka/forma/

http://www.russika.ru/ef.php?s=3346

http://akinfeev.livejournal.com/17482.html?page=26

http://mega.km.ru/bes_2004/encyclop.asp?TopicNumber=34130&rubr=156

http://www.board74.ru/articles/geometry/tcone.html

http://iskystvo.ru/2008/10/

http://flamber.ru/photos/tags/%E4%EE%F0%EE%E3%E0/1181070512/

http://slavyane.cddk.ru/publ/20-1-0-272

http://media.meta.ua/files/pic/0/26/108/mIR6YnZXGo.jpg

pot

orange

animations (lighthouse)

animations (mickey and princess)

frustum

factory pipe

2. Educational institution. Municipal educational institution "Secondary school No. 15 of the village of Berezayka" Bologovsky district of the Tver region

3. Subject, class in which the product is used. Geometry, grade 11

5. Lesson topic. " Cylinder, cone, ball » /PRESS CONFERENCE/

6. Necessary equipment and materials for the lesson. Models of round bodies, "black box" for riddle questions, interactive board to view a presentation or multimedia installation.

7. Description of multimedia product. The presentation was created using the Power Point office application. Change of slides is carried out by mouse click. Content of the presentation: topic of the lesson, goals, followed by slides representing a cylinder, a ball, a cone, a truncated cone, which were created together with students answering questions during a press conference. Next is a slide on which a question of practical content is written, then the answer to it, the results of the lesson and a list of Internet resources. The slides contain pictures and photographs borrowed from the Internet. Formulas, poems compiled by the author of the work

8.The purpose of creating and using a media product in the classroom. For better visibility. The lesson is designed to be open.

9. How is it implemented in the lesson (time and place). It is used at the beginning of the lesson when setting goals and introducing children - representatives of scientific societies: "Cylinder", "cone", "ball", "truncated cone". Then used after summarizing the first part of the lesson, when students begin to complete practical task(fit a sphere into a cube). At the end of the lesson when debriefing.

Bibliography.

1.Altypov P.I. Geometry. Tests. 10-11 cells: educational method. allowance.-M.: Bustard, 2001

2. Ziv B.G. Tasks for geometry lessons grade 7-11. - St. Petersburg, 2000, ed. "Acacia"

3. Geometry: Proc. for 10-11 grades of secondary school / L.S. Atanasyan, V.F. Butuzov, S.B. Kadomtsev and others - M .: Education. 2007