Municipal
Municipal
institution
institution
general education
general education
creative project on the topic of:
Creative project on the topic:
"Christmas ball"
"Christmas ball"
Completed by: 8th grade student
Shabalina Alexandra
Head: Vasilyeva Olga Sergeevna
Inshino 2017
Rationale for choice
Rationale for choice
themesthemes
My school has a very wonderful
teacher - Olga Sergeevna. She teaches us
technologies. Every time we do crafts with her
different topics.
Before the new year, we decided to make a New Year's
ball. We got a very beautiful toy, which
can be hung on Christmas tree or donate
friends, relatives.
Purpose: to make a Christmas ball that will
decorate the Christmas tree.
Product design analysis
Product design analysis
I decided to make this craft because I
attracted by the idea of composition and color scheme
materials
materials
Satin ribbon (yellow) 4cm x 3m Beads Threads
Green fabric Orange fabric Lace
Styrofoam ball
Tools
Tools
Glue gun Scissors Sewing needle
Pencil
carpentry knife
skewers
Historical reference
Historical reference
The oldest iron compass discovered in
France during the excavation of an ancient burial mound. He lay
in the earth for over 2,000 years. In the ashes that fell asleep
Greek city of Pompeii, archaeologists have discovered a very
many bronze compasses. The compass has always been
indispensable assistant to architects and builders.
It is no coincidence that on the facade of one of the most ancient and
beautiful temples of Georgia depicts the hand of an architect, and
behind her is a compass.
Steel compass cutter for drawing such a pattern
archaeologists found during excavations in Novgorod. Is in this
instrument is something that makes it refer to
him with respect. This is how he described meeting him in
Y. Olein’s childhood, author of the famous fairy tale “Three
fat man”: “He lies in a velvet bed, tightly squeezing his legs,
cold sparkling compass. He has a heavy head.
I intend to pick it up. He unexpectedly
opens up and makes an injection in the hand.
IN Ancient Rus' loved the pattern of small circles.
Practical part
Practical part
Prepare in advance: a foam ball,
multi-colored scraps of fabric, lace for
finishes, various satin colored ribbons,
beads, sewing pins, compasses, glue
pistol, clerical knife, scissors and others
improvised means for sewing.
Practical part
Practical part
The pattern on the ball at the very beginning of work is outlined from
line poles. You can use a pen for this
pencil or disappearing marker.
Now all the lines of the pattern should be cut with clerical
knife to a depth of one centimeter. Work needs to be done
very carefully and carefully.
Let's start with the first part of the pattern. To the ball
turned out beautiful, it is better to use pieces of fabric
different shades or two colors so that they can be
alternate. To do this, take pre-cut pieces
of the selected fabric and apply to this part of the pattern.
Practical part
Practical part
At this stage, the fabric should be correctly positioned in
depending on the direction of the pile.
Next, using a skewer or knitting needle, we remove the fabric in
cuts along the entire contour of the selected part of the pattern. Need to
make sure that the fabric lays evenly and does not
warped. It is easier to do this job with
skewers, thanks to which the fabric is removed completely in
slots.
completed, but if you wish, you can continue the work
further. those. give the ball a festive elegant look.
using a glue gun, we will glue a decorative
lace or braid on the borders of the elements of the pattern.
Basically, on this stage, the ball already looks
Practical part
Practical part
First, we coat the joints with glue, and then
put on the tape.
In our case, the finished view of the New Year's ball
will give a bow of narrow braid and gathered lace,
which we will glue together with a bow, but you can use
just a pin. In the center we glue the braid, and already on it
glue beads at equal distances or
buttons. We use a decorative ribbon for hanging.
Safety regulations
Safety regulations
1. Store needles in a pillow or needle bed, wrapping them around
thread. Store the pins in a tightly sealed box.
closing lid.
the box provided for this.
at the end of the work, check their presence.
a pillow, you can not take it in your mouth, do not stick it in clothes,
soft objects, walls, curtains. don't leave
needle in the product.
or working box.
when passing, hold them by closed blades.
scissors.
5. Store scissors in a certain place - in a stand
6. Lay scissors with closed blades away from you;
7. Work well adjusted and sharpened
8. Do not leave scissors with open blades.
9. Monitor the movement and position of the blades during
10. Use scissors only for their intended purpose.
2. Do not throw a broken needle, but put it in a special
3. Know the number of needles, pins taken for work. IN
4. During operation, stick needles and pins into
work.
Economic justification
Economic justification
№
1.
Quantity
in stock
Name
narrow
ribbon (golden)
beads
satin tape
(yellow)
green cloth
orange cloth
Lace
Styrofoam
ball
2.
3.
4.
5.
6.
7.
TOTAL
8 pcs.
4cm x 3m
4 shreds
4 shreds
in stock
1 PC.
Price
----------
15 rub.
15 rub.
35 rub.
35 rub.
----------
45 rub.
145 rub.
ecological
ecological
justification
justification
My work is made of multi-colored shreds
fabrics, using various beads. My product
does no harm environment, because I purchased
materials in specialized stores, this
guarantees the quality. When working with a lighter, I
worked with a teacher and followed all the rules of technology
security. My souvenir is environmentally friendly,
because it does not cause allergic reactions and does not
harms your health.
"Volume of the ball" - Find the volume of the cut-off spherical segment. A sphere is inscribed in a cone with base radius 1 and generatrix 2. Find the volume of a sphere inscribed in a cylinder whose base radius is 1. The volume of a torus. Find the volume of a sphere inscribed in a cube with an edge equal to one. Exercise 22. Find the volume of a ball whose diameter is 4 cm.
"Circumference circle sphere ball" - Ball and sphere. Ball. Circle. Area of a circle. Diameter. Remember how a circle is defined. You need attention, concentration, activity, accuracy. Geometric pattern. The center of the ball (sphere). Try to define a sphere using the concepts of distance between points. Computing center.
"Sphere and ball" - Three points are given on the surface of the ball. Task on the theme of the ball (d / s). A section of a sphere by a plane. Any section of a sphere by a plane is a circle. Tangent plane to sphere. This point is called the center of the sphere, and this distance is called the radius of the sphere. The story of the emergence of the ball. The section passing through the center of the ball is a great circle. (diameter section).
"Balloon balloon" - Since ancient times, people have dreamed of the opportunity to fly above the clouds, swim in the ocean of air. Airships are equipped with low-power and economical diesel engines. It is much easier to raise and lower a balloon filled with hot air. Speed 120-150 km/h. Airships. Aeronautics. Modern world it is difficult to imagine without advertising, and here the use of balloons was found.
"Cylinder cone ball" - The volume of the spherical sector. Find the volume and surface area of the sphere. The definition of a ball. Problem number 3. Areas of surfaces of bodies of revolution. Ball sector. The cross section of a ball with a diametral plane is called a great circle. bodies of revolution. The cross section of a cylinder with a plane parallel to the bases is a circle.
"Scientific-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 Khuzangai 2007. The second school scientific and practical conference dedicated to the 290th anniversary.
Kazakova Daria, Emelyanova Ksenia, Sidorin Andrey
Relevance of the topic: each Small child He loves when his parents buy balloons for him. Various balloons. They can be of different sizes and colors, some can fly away if you let him go, while others fall to the ground. But not every child knows when the balls appeared, what they are made of.
Hypothesis: any balloon is made of a material that, when any substances enter it, increases in size. Goals: Learn the history of the balloon. Research objectives: - collect information who invented the first ball; - What are balloons made of? What are balloons? - what balloons are used for. - under what conditions balloons can change their size.
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The work was completed by: students of the 4th "B" class of the GBOU secondary school No. 2017 Emelyanova Ksenia, Kazakova Daria, Sidorin Andrey. "Secrets hot air balloon»
Relevance of the topic: every little child loves when parents buy balloons for him. Various balloons. They can be of different sizes and colors, some can fly away if you let him go, while others fall to the ground. But not every child knows when the balls appeared, what they are made of. Hypothesis: any balloon is made of a material that, when any substances enter it, increases in size. Objectives: Learn the history of the appearance of the balloon. Research objectives: - to collect information about who invented the first ball; What are balloons made of? What are balloons? What are balloons used for? Under what conditions can balls change their size. 18.1.15
What is a hot air balloon? A balloon is not only a toy, without which no holiday can do, it is mainly used for decorating rooms and holidays. Balloon - aircraft(aerostat), in which a gas lighter than air is used for flight. 18.1.15
When and where did the first ball appear? The first balloons were made from animal bladders (pigs). Modern balloons were born in 1824. They were invented by the English scientist Michael Faraday.
What is helium? Helium is one of the most abundant elements in the universe, second only to hydrogen. Helium is also the second lightest (after hydrogen) chemical substance. Helium is widely used in industry and the national economy: for filling aeronautical vessels (airships and balloons) - with a slight loss in lift compared to hydrogen, helium is absolutely safe due to its incombustibility; in breathing mixtures for deep-sea diving; to fill balloons Hydrogen is the most abundant element in the universe. Hydrogen is the lightest gas. Hydrogen is widely used in many industries: chemical (soaps and plastics), food (margarine made from liquid vegetable oils), aviation (hydrogen is very light and always rises in the air. Once airships and balloons were filled with hydrogen), in meteorology (to fill balloon-pilot shells), hydrogen is used as rocket fuel. 18.1.15
What are balloons made of today? Balloons are made from latex and foil. 18.1.15
What is latex? Latex is the processed sap of the Hevea rubber tree. What is foil? Foil - metal "paper", a thin and flexible metal sheet.
Types of balloons Classic latex balloons Modeling balloons Wrapping balloons Milar (foil) balloons Walking foil figures Self-blowing balloons Flying balloons
Flying balloons. With the help of balls, in the old days they partially solved the problem of off-road. During the war, balloons were used as aerial observation posts and barriers to protect cities from bomber raids. Today, balloons are mainly used to explore the upper atmosphere, to obtain information about the weather.
What can you use to inflate balloons? 1.Manual pump. 2. Electric pump. 3. Gel. 4. Lips. 5. With the help of baking soda and table vinegar (only with the help of adults)
18.1.15 Experience 1. Conclusion: any latex balloon, when inflated, changes its size, and when the air begins to escape, the balloon shrinks and becomes the same as it was before the start of the experiment.
18.1.15 Experience 2. . Conclusion: This experiment proves that latex balloons are made of a material that allows you to change the size, that they are very durable.
Experiment 3. 18.1.15 Conclusion: this experiment proves that it is better to inflate foil balloons with the help of special devices.
18.1.15 Conclusion: before the experiment, we thought that a foil ball with water would burst, but this experience proves, this experiment proves that foil balls are made of such a material that allows you to change the size when any substance is placed inside, that they are durable. Experience 4.
Conclusion: Using baking soda and vinegar, you can inflate a balloon at home. Experience 5.
Let's compare latex and foil balloons. Foil balloons Foil balloons are more durable. Thanks to the material from which foil balloons are made, they hold both air and helium longer, so they stay inflated longer. Foil balloons are thicker than latex balloons and are not so afraid of roughness Latex balloons Due to the elasticity of latex, latex balloons can take the most unusual shapes. Latex balloons can be filled with both air and helium. They can be inflated manually or with a special compressor. Balloons made of latex become transparent when inflated, while those made of foil do not 18.1.15
Conclusions: As a result of the study, we found out: what balloons are made of different materials; that the balloon is made of latex and foil, when water, air, helium and hydrogen enter it, it increases in size; that balloons filled with gas are lighter than balloons filled with air, so they rise no matter what the balloons are made of. that balloons are currently used to decorate halls, as toys for children, as well as for flights and research. 18.1.15
The used literature Big encyclopedia of the schoolboy. M.: CJSC "ROSMEN - PRESS", 2010. Everything about everything. Encyclopedia for children - M .: "Slovo", 2009. Encyclopedia of the student. 4000 very important facts. M: Moscow "Makhaon", 2006. Internet resources: material from Wikipedia - the free encyclopedia
Sphere and ball
creative project name
The many faces of "Round bodies"
Subject, class
Geometry, grade 11
Brief summary of the project
In life, we often use the words sphere, ball. During the work on the project, you will get acquainted with the scientific concepts of a sphere, a ball and their elements, in the future you will correctly use these terms. Having derived the equation of a sphere, you will learn how to write it for a given center and radius and, conversely, determine whether the surface is a sphere using the equation. It will be interesting enough to consider all possible cases of the location of a sphere and a plane, to get acquainted with the definition of a tangent plane to a sphere and theorems expressing the properties and sign of a plane tangent to a sphere. Learn the formula for calculating the area of a sphere. And, of course, you will learn how to solve problems on this topic, both compulsory and advanced.
For centuries, humanity has not ceased to replenish its scientific knowledge in a particular field of science. Many learned geometers, and indeed ordinary people, were interested in such a figure as a ball and its “shell”, called the sphere. Many real objects in physics, astronomy, biology and other natural sciences are spherical in shape. Therefore, the study of the properties of the ball was assigned in various historical epochs and is assigned a significant role in our time.
I wish you success!
Reflective Blog
Guys, write your feedback after each stage of the project in a reflective blog
Guiding questions
Fundamental question
How to explore the laws and patterns of the Universe?
Problematic issues
- What is the relationship of geometry with other fields of science?
- What are round bodies associated with?
- Why were many geometers interested in such a figure as a ball and its “shell”, called a sphere?
Study questions
- Define a sphere and a sphere. What do they have in common and what is the difference?
- How can a sphere and a ball be obtained?
- How to write the equation of a sphere if its center and radius are given?
- How many possible cases of mutual arrangement of a sphere and a plane? What does it depend on? Sections of a sphere and a ball.
- What plane is called the plane tangent to the sphere? What is its main property? Is it possible to determine if a given plane is tangent to a sphere?
- Sphere area formula.
- Mutual position of a sphere and a straight line.
- Ellipse, hyperbola, parabola as sections of a cone.
- A sphere inscribed in a polyhedron, a sphere circumscribing a polyhedron.
Project Plan
Project business card
Teacher publication. Parent booklet
Teacher presentation to identify student perceptions and interests
Working groups and research questions
Group “Mathematicians” Belyakova Maria, Kobeleva Alena, Morozova Yulia
Summarize the material on the topic “Sphere and ball”, studied in the school geometry course;
Find and compare all definitions of a sphere and a ball;
Prepare summary tables, a collection of tasks.
Group "Geographers" Alena Kononykhina, Albina Prokofieva, Maxim Samorodov
Find the first mention of the Earth as a spherical surface;
Find materials pointing to the evolutionary development of planet Earth.
Group "Astronomers" Eremin Vladislav, Kuzmin Evgeny, Pavlochev Ilya
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" Gogoleva Anastasia, Pukosenko Victoria, Chernova Julia
Find the 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.
Art critics group Zhaksalikova Nadezhda, Kabanina Julia, Chemis Valentina
Find paintings, engravings that depict a sphere.
Group “Scientific Council” Marina Astanayeva, Irina Balaeva, Yulia Rostunova
Conduct an analysis of the tasks of the exam. Select assignments for this topic. Select tasks for the final repetition.
Suggested topics for student projects
"The Mutual Position of a Sphere and a Plane"
"Ball and Sphere"
"The ball is a symbol of God"
"Harmony of the ball"
"Music of the Sphere"
"Sphere and ball in architecture"
"Sphere and ball in the world around us"
Email addresses of project participants
I ask all project participants to enter their data in the table after completing registration on the Gmail mail service
Some materials of the theoretical seminar
The results of the project activities of students
Materials for formative and final assessment
Materials for support and support of project activities
Useful Resources
Theoretical material
Sphere. Dictionaries and encyclopedias at Academic Shar. Dictionaries and encyclopedias on Academician Models of lessons. Sphere and ball. Touches and sections. Parts of a ball and a sphere Sphere and a ball. Sections of a sphere and a sphere by a plane. Tangent plane to sphere. Ball and sphere. Abstract. Sphere
slide 2
A sphere is a surface that consists of all points in space that are at a given distance from a given point. This point is called the center, and the given distance is called the radius of the sphere, or ball - a body bounded by a sphere. A ball consists of all points in space that are at a distance not greater than a given point from a given point.
slide 3
The segment connecting the center of the ball with a point on its surface is called the radius of the ball. The segment connecting two points on the surface of the ball and passing through the center is called the diameter of the ball, and the ends of this segment are diametrically opposite points of the ball.
slide 4
What is the distance between diametrically opposite points of the ball if the distance of a point lying on the surface of the ball from the center is known? ? 18
slide 5
A sphere can be considered as a body obtained from the rotation of a semicircle around the diameter as an axis.
slide 6
Let the area of the semicircle be known. Find the radius of the ball, which is obtained by rotating this semicircle around the diameter. ? 4
Slide 7
Theorem. Any section of a sphere by a plane is a circle. A perpendicular dropped from the center of the ball to the cutting plane falls into the center of this circle.
Given: Prove:
Slide 8
Proof:
Consider a right-angled triangle whose vertices are the center of the ball, the base of the perpendicular dropped from the center to the plane, and an arbitrary section point.
Slide 9
Consequence. If the radius of the ball and the distance from the center of the ball to the plane of the section are known, then the radius of the section is calculated using the Pythagorean theorem.
Slide 10
Let the diameter of the ball and the distance from the center of the ball to the cutting plane be known. Find the radius of the circle, the resulting section. ? 10
slide 11
The smaller the distance from the center of the ball to the plane, the greater the radius of the section.
slide 12
A sphere of radius five has a diameter and two sections perpendicular to this diameter. One of the sections is at a distance of three from the center of the ball, and the second is at the same distance from the nearest end of the diameter. Mark the section with the larger radius. ?
slide 13
Task.
Three points are taken on a sphere of radius R, which are the vertices of a regular triangle with side a. How far from the center of the sphere is the plane passing through these three points? Given: Find:
Slide 14
Consider a pyramid with a top in the center of the ball and a base - a given triangle. Solution:
slide 15
Let's find the radius of the circumscribed circle, and then consider one of the triangles formed by the radius, the side edge of the pyramid and the height. Let's find the height using the Pythagorean theorem. Solution:
slide 16
The largest sectional radius is obtained when the plane passes through the center of the ball. The circle obtained in this case is called the great circle. The large circle divides the ball into two hemispheres.
Slide 17
Two great circles are drawn in a sphere whose radius is known. What is the length of their common segment? ? 12
Slide 18
Plane and line tangent to the sphere.
A plane that has only one point in common with a sphere is called a tangent plane. The tangent plane is perpendicular to the radius drawn to the tangent point.
Slide 19
Let a ball whose radius is known lie on a horizontal plane. In this plane, through the point of contact and point B, a segment is drawn, the length of which is known. What is the distance from the center of the sphere to the opposite end of the segment? ? 6
Slide 20
A line is called a tangent if it has exactly one point in common with the sphere. Such a straight line is perpendicular to the radius drawn to the point of contact. An infinite number of tangent lines can be drawn through any point on the sphere.
slide 21
Given a sphere whose radius is known. A point is taken outside the ball, and a tangent to the ball is drawn through it. The length of the tangent segment from a point outside the ball to the point of contact is also known. How far from the center of the sphere is the outer point? ? 4
slide 22
The sides of the triangle are 13cm, 14cm and 15cm. Find the distance from the plane of the triangle to the center of the ball touching the sides of the triangle. The radius of the ball is 5 cm. Problem. Given: Find:
slide 23
The section of the sphere passing through the points of contact is the circle inscribed in the triangle ABC. Solution:
slide 24
Calculate the radius of the circle inscribed in the triangle. Solution:
Slide 25
Knowing the radius of the section and the radius of the ball, we find the required distance. Solution:
slide 26
Through a point on a sphere with a given radius, a great circle and a section are drawn that intersect the plane of the great circle at an angle of sixty degrees. Find the sectional area. ? π
Slide 27
Mutual arrangement of two balls.
If two balls or spheres have only one common point, then they are said to touch. Their common tangent plane is perpendicular to the line of centers (the straight line connecting the centers of both balls).
Slide 28
The contact of the balls can be internal and external.
Slide 29
The distance between the centers of two touching balls is five, and the radius of one of the balls is three. Find the values that the radius of the second ball can take. ? 28
slide 30
The two spheres intersect in a circle. The line of centers is perpendicular to the plane of this circle and passes through its center.
Slide 31
Two spheres of the same radius equal to five intersect, and their centers are at a distance of eight. Find the radius of the circle where the spheres intersect. For this, it is necessary to consider the section passing through the centers of the spheres. ? 3
slide 32
Inscribed and circumscribed spheres.
A sphere (ball) is said to be circumscribed near a polyhedron if all the vertices of the polyhedron lie on the sphere.
Slide 33
What quadrilateral can lie at the base of a pyramid inscribed in a sphere? ?
slide 34
A sphere is called inscribed in a polyhedron, in particular, in a pyramid, if it touches all the faces of this polyhedron (pyramid).
Slide 35
At the base of a triangular pyramid lies an isosceles triangle, the base and sides known. All side edges of the pyramid are equal to 13. Find the radii of the circumscribed and inscribed spheres. Task. Given: Find:
slide 36
Stage I. Finding the radius of the inscribed sphere.
1) The center of the described ball is removed from all the vertices of the pyramid at the same distance equal to the radius of the ball, and in particular, from the vertices of the triangle ABC. Therefore, it lies on the perpendicular to the plane of the base of this triangle, which is reconstructed from the center of the circumscribed circle. In this case, this perpendicular coincides with the height of the pyramid, since its side edges are equal. Solution.
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