Cylinder as a geometric figure. Cylinder shaped objects What are cylindrical objects
However, scientists not only made the male sexual organ the subject of their research, but also classified the varieties of the genitals. We want friends, classmates, classmates, neighbors and colleagues to always stay in touch. Find objects in the environment that can serve as models. For the academic year, the amount of the registration fee per participant for one of the proposed subjects is set at 75 rubles. You can circle some round object, for example, the bottom of a plate. Encourage yourself to combine different techniques to enhance expressiveness. In any case, this form, according to firefighters, is very convenient. From D beyond at 0957, say platform big light. And these objects most often have the shape of either a straight circular cone or a shape. A lamp with a metal shade casts a beam of light in the form of a cone. Looking at these attributes, people pass by, and only the most curious wonder why the fire bucket is shaped like a cone. Free download Lesson summary Cylinder. Equipment mm projector, video sequence, objects in the form of cones and truncated cones, Rocket toy, coffee pot, cap from the New Year's costume Mag
VKontakte is a universal tool for communicating and finding friends and classmates, which is used by tens of millions of people every day. What objects in the form of a cone and a cylinder does the tailor use in his work? Painting Autumn in the form of a cloud 1 12x18. The production of this item is not creation. Let's arrange the object in space so that each of the two parallel to each other. D such as a cube, pyramidal figures of various shapes, trapezoid, oval, octahedron, cylinder, cone, prism. Name all objects in the form of a cylinder and a cone. I can't find it here. Objects in a still life, which are based on bodies of revolution, are enough so, with frontal lighting of a still life instead of a form. Sculpting Icicles Imagination To teach children to sculpt objects in the shape of a cone. Screenwriter, director, cameraman and m. It is very clearly seen how the shadow intensifies towards the top and weakens towards the base of the cone. Thanks to the cutting of such a bucket in the shape of a cone, it takes much less tin and is easier technological. Equipment spherical objects, a set of photographs and drawings of spherical objects, a cylinder, a cone
Slide 21 Questions on polyhedra. Math lesson on the topic Cone in grade 4. A cylinder is a geometric body bounded by a cylindrical surface and two parallel planes intersecting e at a right angle. What is in the black box? To form an idea of a cylinder, the ability to recognize a cylinder in objects. A cone, unlike a cylinder, has a vertex showing. Guys, to whom I will now throw this ball, you need to give your own example of an object that has the shape of a ball. At first I bought 1 lampshade in the shape of a cone S for trial. Diam at the bottom 35 cm Height 18 cm. White-red such a small traffic cone. Let us give examples of objects having the shape of 1 cylinder 2 cones 3 balls. Strengthen the ability to find an object in different places. Form of objects in English.
In the 19th century, in parallel with the theory of systems of linear equations, the theory of vectors developed. In 1903, O. Henrichi suggested that the scalar product be denoted by the symbol (a, c). Check yourself! Decomposition of a vector in coordinate vectors. The simplest problems in coordinates. The concept of a vector. The coordinate vectors are directed along the coordinate axes. A vector is a directed segment. Story. Decomposition of a vector on a plane in two non-collinear vectors.
"The radius of the inscribed and circumscribed circle" - Circle and triangles. Basic formulas for regular polygons. The circumscribed circle about a quadrilateral. Parallelogram. Circle. Trapeze. An inscribed circle in a quadrilateral. circumscribed circle. Inscribed and circumscribed circles. Inscribed circle. Circle and regular polygons. Convex polygon. Circle and right triangle.
"Method of the golden section" - Golden proportion - harmony and beauty. The history of the golden section. The rule of the golden section is quite applicable to portraits. golden rectangle. Golden ratio in mathematics. Are people harmonious? Golden section in painting. The Golden Ratio in Sculpture. Our tasks. Portrait photography. Golden spiral in nature. Division of a line segment according to the golden ratio. Proportionality in nature, art, architecture.
"Properties of a triangle" - Middle line. Median. Bisector. Properties of bisectors. The square of the side of a triangle. Proof. Similar triangles. Right triangle. Sine theorem. Types of triangles. Arbitrary triangle. Figure. Triangle. Signs of equality of right triangles. The median drawn to the base. Height. Equilateral triangle. median perpendicular. Theorem. Signs of equality.
""Method of coordinates" class 9" - Point M1 (x1; y1) does not belong to the circle. Let's prove the formula. Consider an example. Find the coordinates of the points. Formula. Let's use equalities. Point coordinates. Segment AB is parallel to axis OY. Circle equation. Isosceles right triangle. coordinate method. The coordinates of the middle of the segment. Midpoint C of segment AB. Points of intersection of the coordinate axes. Equation of the first degree. Let's use the formula to find the distance.
"Circle Equation" Grade 9 "- Circle. Write an equation for a circle. Draw the circles given by the equations in your notebook. Write an equation for a circle with a center. Circle equation. Lesson goals. Construct circles in a notebook according to the data obtained. Formula derivation. Find the coordinates of the center and the radius. Center coordinates. Fill the table. Circle center. Circle point coordinates. Write down the formula. Group work. Origin.
Straight circular CYLINDER Lateral surface Bases of the cylinder О1О1 О ά β Cylinder axis generating h (height) r (radius) Definition: A right circular cylinder is a cylinder whose base is equal circles, and the generatrix is perpendicular to the bases ά||β
3. The radius of the cylinder is the radius of its base 4. The height of the cylinder is the distance between the planes of the bases in a straight cylinder, it coincides with the generatrix 5. The axis of the cylinder is a straight line passing through the centers of the bases, It is parallel to the generators. 1. The lateral surface of the cylinder is called the part of the cylindrical surface enclosed between parallel planes 2. The bases are part of the planes cut off by the cylindrical surface,
AD BC Fig.1 A straight circular cylinder can be obtained by rotating a rectangle around one of its sides. in Figure 1 - the cylinder is obtained by rotating the rectangle ABCD around the side AB in Figure 2 - the cylinder is obtained by rotating the rectangle ABCD around the side AD A D B C Fig.2
ABB 1 A 1 - rectangle B A1A1 B1B1 A 2πr2πr h S side = 2πrh S full = S side + 2 S main => S full = 2πrh + 2πr² = 2πr (r + h) Lateral and full surface of the cylinder h A B r S full \u003d 2πrh + 2πr² \u003d 2πr (r + h) Lateral and full surface of the cylinder h A B r "> S full \u003d 2πrh + 2πr² \u003d 2πr (r + h) Lateral and full surface of the cylinder h A B r"> S full \u003d 2πrh + 2πr² \u003d 2πr (r + h) Lateral and full surface of the cylinder h A B r "title=" (!LANG:ABB 1 A 1 - rectangle B A1A1 B1B1 A 2πr2πr h S side = 2πrh S full = S side + 2 S main => S full \u003d 2πrh + 2πr² \u003d 2πr (r + h) Lateral and full surface of the cylinder h A B r"> title="ABB 1 A 1 - rectangle B A1A1 B1B1 A 2πr2πr h S side = 2πrh S full = S side + 2 S main => S full = 2πrh + 2πr² = 2πr (r + h) Lateral and full surface of the cylinder h A B r"> !}
H r h1h1 r1r1 “The side and full surfaces of similar cylinders are related as squares of radii or heights” Theorem: Definition: “Cylinders are called similar if they originated from the rotation of similar rectangles” S side 1 = r 1 ² = h1²h1² S side r²h² = S full S full 1
Problem First option Calculate the total and side surfaces of a cylinder obtained by rotating a square with a side equal to 1 cm (give the answer without calculating the value of π) Second option Calculate the total and side surfaces of a cylinder whose radius is 1 dm and height 2 dm (answer is given , without calculating the value of π)
Answer the questions 1. Name the elements of the cylinder 2. Name the type of axial section of the cylinder 3. Can the section of the cylinder be: a rectangle a square a trapezoid? 4. Which of these statements are true: any section of a cylinder by a plane perpendicular to the base is a circle equal to the circumference of the base; any section of a cylinder by a plane is a circle equal to the circumference of the base; a plane perpendicular to the axis of the cylinder intersects it in a circle equal to the base of the cylinder; the cross section of a cylinder can be a circle, a rectangle, an ellipse.
Answer the questions 1. Name the elements of the cylinder (side surface, base, axis, radius, generatrix, height). 2. Name the type of axial section of the cylinder 3. Can the section of the cylinder be: - a rectangle (yes) - a square (yes) - a trapezoid? (no) 4. Which of these statements are true: - any section of the cylinder by a plane perpendicular to the base is a circle, equal to the circumference of the base; (incorrect) - any section of a cylinder by a plane is a circle equal to the circumference of the base; (incorrect) - a plane perpendicular to the axis of the cylinder intersects it in a circle equal to the base of the cylinder; (correct) - the section of a cylinder can be a circle, a rectangle, an ellipse. (correct)
List of materials used 1) Textbook "Geometry 10-11", L.S. Atanasyan et al., Moscow, Enlightenment) Handbook of Mathematics A.A. Ryvkin et al., Moscow, Higher School) Mathematics. Reference materials V.A. Gusev, A.G. Mordkovich Moscow, Enlightenment) Encyclopedic Dictionary of a Young Mathematician Moscow Pedagogy 1989 Author: Schukina Irina Vladimirovna Mathematics teacher YaNAO, Nadym, secondary school 5
Picture 3 from the presentation "Cylinder"
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"Description of the subject" - Questions: Speech styles. "Preparation for the essay" Description of the subject ". Dictionary. Lesson topic: Ski competitions. Types of speech. Objectives: Write an essay - a description of "My favorite subject." Plan. Skiers training. Skiers. The description is divided into 3 parts: Description.
"School subjects" - "History". The hours allocated to the educational component are used for: Life Safety Fundamentals. The introduction of 1 hour / week is recommended. from the hours of the school component - grade 11. E) independent work of students in laboratories, libraries, museums. Biology and geography.
"Main subjects" - Repetition. Geometry. Chemistry. Economy. Physics thermodynamics electrostatics. Geography. Russian language English language Geography Literature History. Physics. Geography of the world Geography of Russia Geography of Europe Geography of Asia. Story. English language. Practical English Spelling Grammar. Economy of the world Economy of Russia Economy of Europe Economy of Asia.
"Items in Grade 1" - Fruits. Insects. Big, tasty, sweet, festive, covered with cream. Guess the item from the description. Green, prickly, forest, high. Decide which group you belong to. Describe the item. Vegetables. Learning to combine things. Red, round, smooth, juicy.
"Words-objects" - Table House Cat Coat Eskimo Pony hand. Words are neuter things. Words are feminine. Apples. House tables Cats Eskimo coat Pony hands. Apple. Words are masculine. Plural. Change by numbers. Words are things. What? Singular. Words are things. Words are things.
All cylindrical objects have a vertical axis of symmetry, and their side surfaces are at the same distance from the center and seem to form a circle if you look at such an object from above. In perspective, the circle looks like an ellipse. How to build it? Let's try to fit a circle into a square and draw diagonals. We will get that the circle will intersect the diagonals at a distance of approximately 1/3 of their length and will touch the square at the centers of its sides. Now, if we draw a square with diagonals in perspective and then try to inscribe a circle into it at the same points, we will get an ellipse, because, like a square, a circle in perspective will take on the form of an elongated figure.
To draw a cylinder, you must first draw an axis of symmetry. Then, with two horizontal lines above and below, limit its height, and on the horizontal lines indicate the width of the cylinder. After that, build planes into which the ellipses will “fit” over time.
Since in the cylinder the side surface seems to rotate around its axis, the rays of light fall on it all the time at a different angle. There is a gradual change in light and shade ratios over the entire height of the figure. In the middle of the illuminated part there is a long vertical highlight, then the light gradually passes into partial shade and further into shadow. The shadow becomes lighter, turning into a reflex. According to this principle, the form is built and the chiaroscuro of all cylindrical objects is transmitted: cups, buckets, etc.
Constructing a circle and an ellipse
Start building a cylinder
Finished work
The surface of the sphere is curved at any point. It is relatively easy to build such a figure (see the figure for constructing a circle and an ellipse). It is much more difficult to depict the volume of the ball, because the rays of light fall on its surface in different parts at different angles. We can only conditionally select an ellipse that separates the light and shadow parts of the ball. Light passes into penumbra evenly in all directions. The highlight is in the center of the illuminated part. A reflex appears on the shadow half of the ball. The drop shadow is placed under the figure and is shifted to the side opposite to the illuminated side of the object. Knowing how to build a ball, it is easy to depict spherical objects, such as a ball, watermelon, orange, apple. Having learned how to draw simple geometric bodies: a cube, a cylinder, a ball, we can move on to more complex tasks.
ball drawing
A jug is an object that combines a cylinder and a ball in its shape.
Apples are spherical
Jug with mug. The hole of both objects is depicted as an ellipse. Light falls from the left side. Own shadow and drop shadow are on the right
The French artist Paul Cezanne stated: "All objects around us fit into one or another simple geometric body." Therefore, starting the construction of any object, one must carefully look at what geometric figure it is similar to. This will help determine its design.
- How are tone changes similar and different on cylindrical and spherical objects?
- Tell us what simple geometric shapes are combined in a jug.
Draw a ball or other spherical object (for example, an apple) or a cylinder glued from paper, illuminating it with artificial light.
Tools and materials: sheet of paper, graphite pencil, eraser.
Work plan:
- Compose the image on a piece of paper.
- Compare the proportions of different parts of the image each separately: height to width.
- Fix build errors.
- Determine which surface is lit brighter and how the background looks next to the subject.
- Take a closer look at where the shadow is darkest and how the tone of the background has changed in the shadow.
- Observe different halftone ratios on surfaces differently inclined towards the light source.
- Recreate the difference in tone on the subject. Where is the greatest contrast created?
Stages of work on a drawing
Remember the main rule: you need to draw from the general form to its parts and details. It is important to be able to see everything as a whole, and details, details will appear gradually in the process of work.
- At the first stage of work, it is necessary to determine the placement of the image on the sheet - the composition. To do this, determine the largest width and height of the entire image (all parts of the nature that you will draw), the distances from the extreme borders to the right and left, from the highest to the lowest. Having thus limited the area on which the image will be placed, you can easily outline its main proportions with two or three lines.
- At the second stage, it is necessary to more accurately determine the place of each part, compare them with each other, that is, their sizes, proportions, design (axis of symmetry, if any, similarity with a geometric figure). To make it easier to analyze nature, you can ask yourself the question: “Which part of the object is the largest?”, “What is the smallest?”, “What is located above all?” etc. To make it easier to build objects, they should be drawn as if with “transparent”, light lines.
- At the third stage, try to refine the shape of the object, start working in tone. It is necessary to make a light tone lining in all the shadows at the same time with a stroke, to determine the “big shadow”. Then move on to a detailed tonal study of each detail of the subject. At this stage, it is important to constantly compare which part is darker, which is lighter, where the background is darker than the subject, and where it is vice versa.
- At the final stage, it is important to analyze all the work. It is necessary to check the correctness of tonal relationships, the construction of objects, whether the texture of the material from which the object is made, its volume is conveyed in the figure.
You should be sure to determine which place in the picture is the lightest, which is the darkest, where the greatest contrast is observed. That is, starting work from the “general”, we go to specific details, and then, at the last stage, we again return to the “general”.
Stages of work on a drawing
Brothers Limburg(Manuel, Paul, Ermann, Enneken) - French (Dutch) artists of the 15th century. They worked at the court of the Dukes of Burgundy and Berry. The main work of the Limburg brothers is The Magnificent Book of Hours of Duke Jean of Berry (c. 1418), for which they made 71 miniatures. Miniatures dedicated to the months of the year depict scenes from life - a feast (January), a betrothal (April), a falconry trip (August); there are among them depicting peasant life - “peasants at the hearth” (February), “sowing winter crops” (October).
The Limburg Brothers. Book of hours. The battle of the archangel Michael with the dragon
Yakutovich Georgy Vyacheslavovich(1930-2000) - Ukrainian graphic artist. He was engaged in easel graphics and book illustration. In the 1960s, he turned to the principles of designing a book as an integral work of art. The ability to convey a literary idea in black and white and color, a clear, confident drawing, the rhythm of lines made the work of G. Yakutovich a model for many domestic illustrators in the 1960s and 1970s. Among the best works of Ukrainian book graphics, a prominent place belongs to such works by Yakutovich as illustrations for the plays by I. Kocherga "Yaroslav the Wise" and "Svichka's Wedding", M. Kotsyubinsky's story "Shadows of Forgotten Ancestors", outstanding historical works "The Tale of Igor's Campaign" , "The Tale of Bygone Years".
G. Yakutovich. Illustration for M. Kotsiubsky's story "Shadows of Forgotten Ancestors"