On the world map hemispheres the smallest distortion has. We look and think. Classification of projections by distortion

1. Distortions are the less, the smaller part of the surface of the globe is shown on the map. Topographic maps covering very small sections of the earth's surface, on which the bulge of the Earth is not noticeable, give the most accurate images.

2. In different parts of the same map scale different. Scale at points or on zero distortion lines are called the main scale. It is usually indicated on the maps. When the zero distortion from the points or the zero distortions, the map scale is increasingly different from the main one. Only on topographic maps indicated on them is valid for all parts of them.

3. The smallest distortions on the maps - in their midblars, with the removal of the distortion cards to the edges (frame) increases.

Distortion on the hemisphere cards. To find out which distortions turned on the hemispheres on the map, it is necessary to compare the degree grid of the globe and the map mesh map. On the globe, all meridians have the same length, which corresponds to reality. On the map of hemispheres the length of meridians is different. The average meridian is depicted straight line, the rest - curved. The further the meridians are located from the average, the more they are curved, and the extreme form a semi-rareness and almost one and a half times longer than the average meridian parallels on the globe are depicted in the form of circles parallel to each other. On the map hemispheres Equator - straight line, and parallels - arcs, and the distance between adjacent parallels of the unequal and increase to the edges of the card.

Let's see what is the location of the meridians and parallels on the hemispheres map and how it is reflected in the objects depicted. On the globe section of the earth's surface (ocean or sushi) near the equator, having a length of 10 ° in latitude, everywhere has a figure similar to a square. On the map of the hemispheres these sections on different longitudes have different figures. In the center they have a form close to the square, as well as on the globe, and to the edge of the map, their form changes greatly. In this case, the segments of the meridians are lengthened, and the segments of the equator are shortened

From all this it follows that distances that are the same on the globe (land), in different places of the card are depicted by segments of different lengths, i.e., the scale of the map of the neodynaks in different parts. So it turns out the difference in the cartographic image.

The scale specified on the maps is accurate not for the entire card, but only for its specific parts. Therefore, it is impossible to use it when measuring distances and areas. On the map, the semisses scale corresponds to the indicated only at the central point, namely at the point of intersection of the equator and the average meridian. This is a point of zero distortion. In all other parts of the map, the scale is greater than or less specified on it. On other maps may not point, but the line of zero distortion.

Distortion on world maps. On world distortion maps, the largest, since they are depicted the surface at once. For example, on a globe of 1 ° longitude at 60 ° C. sh. and Yu. sh. It is 55.8 km, i.e., two times less than at the equator. On the world map, this distance is only 1.5 times. 1 ° longitude 80 ° C. sh. and Yu. sh. For less than the equator, already 6.5 times, and on the world map only 2 times. The scale specified on these world maps is stored in parallel to 45 ° C. sh. and Yu. sh. According to the parallels lying from them towards the equator, it is less, and in the side of the poles - more. And to the poles he increases rapidly. Therefore, in the northern and southern parts of our world maps, geographicals are noticeably stretched from west to east. In terms of meridians, the scale indicated on world maps is stored only in the center - at the intersection of the average meridian and equator. With the removal in all directions the scale of lengths in meridians increases. Therefore, the length of the segments of meridians between parallels increases.

All-Russian Olympiad Schoolchildren in Geography

Iemunicique Stage, 2014

Class.

Total time - 165 min

Maximum possible score - 106

Test round (time for execution 45 min.)

It is forbidden to use atlas, cellular and Internet! Good luck!

I. From the proposed answers options, select one faithful

What scale can be done by the "Natural Zones of the World" in the Atlas for 7 CL?

a) 1: 25000; b) 1: 500000; c) 1: 1000000; d) 1: 120 000 000?

2. On the world map hemisphere the smallest distortion has:

a) o-in fiery land; b) O-Va Hawaiian; c) rs indochina; d) rs Kolsky

3. In one degree of the circle of the equator, in comparison with other parallels, contains:

a) the largest number of kilometers, b) the smaller number of kilometers, c) as much as and on the rest of the parallel

On the territory of which bay is the point of reference and longitude on the map?

a) Guinean, b) Biscay, c) Californian, d) Genoese.

5. Kazan has coordinates:

a) 45 O 13 / S.Sh. 45 O 12 / V.D., b) 50 o 45 / S.Sh. 37 o 37 / V.D.,

c) 55 o 47 / s.sh. 49 O 07 / V.D., D) 60 O 13 / S.Sh. 45 O 12 / V.D.

On the terrain, tourists are moving focusing on

a) magnetic azimuth, b) geographical azimuth, c) True azimuth, d) Rumba.

What azimuth corresponds to the direction on the SE?

a) 135º; b) 292.5º; c) 112.5º; d) 202.5º.

What azimuth you need to move if the path lies from the point with the coordinates

55 0 S.Sh. 49 0 V.D. to the point with coordinates 56 0 S.Sh. 54 0 VD?

a) 270 0; b) 180 0; c) 45 0; d) 135 0.

What kind of meridian can be focused on eye shooting?

a) geographical, b) axial, c) magnetic, d) zero, e) in all together

10. What time of year on the islands of Svalbard, when the earth's axis turns to the sun with the northern end? a) autumn, b) winter, c) summer, c) spring.

11. At the time when the earth is most removed from the Sun, in Kazan:

a) the day longer night, b) the night is longer than the day, c) the day is equal to the night.

In which hemisphere, the polar day lasts longer?

a) in southern, b) in northern, c) in western, d) in east

13. In which month, the tropical latitudes of the southern hemisphere get the greatest amount of solar heat? a) January, b) March, c) June, d) September.

With what weather is the daily air temperature amplitude, is big?

a) cloud, b) cloudless, c) cloudiness does not affect the average daily temperature amplitude.

15. In which latitudes are the highest absolute air temperatures fixed?

a) Equatorial, b) tropical, c) moderate, d) arctic.

16. Determine the relative humidity of the air having a temperature of 21 ° C if it contains 40 g of water vapor in its 4 cubic meters, and the saturated water vapor density at 21 o C corresponds to 18.3 g / m 3.

a) 54.6%, b) 0.55%, c) 218.5%, d) 2.18%.

17. At the airport of Sochi air temperature +24 ° C. The plane rose into the air and took the direction to Kazan. Determine the height at which the aircraft flies if the air temperature beyond its side -12 ° C.

a) 6 km, b) 12 km, c) 24 km, d) 36 km.

What will be the atmospheric pressure on the talvega ravine, if atmospheric pressure equal to 760 mm.Ret was recorded in the upper part of the slope, and the depth of the incision of the ravine is 31, 5 m.

a) 3 mm.tr.st., b) 757 mm.rt.st., c) 760 mm.rt.st, d) 763 mm.rt.st.

a) St. Lavraventia, b) Fandy, c) Obba, d) Penzhinskaya Guba.

20. Name the mainland, which is both part of the light and the continent, and is located in four hemispheres:

a) America, b) Africa, c) Australia, d) Antarctica, e) europe, e) asia, g) Eurasia, s) Y.America, and) S.Amerik

The most western point of Asia - Cape

a) Piaay, b) Chelyuskin, c) Baba, d) Dezhneva.

Continental shelf practically absent

a) in the western coast of Y.Ameriki, b) from the northern shores of Eurasia,

c) from the western coast of S.Ameriki, d) near the northern shores of Africa.

Earth Bark is a more young in the area

a) lowlands, b) the mid-ocean ridges, c) of low mountains, d) oceanic kitelins.

The source of the Volga River is located

a) in the Midnesday region, b) in the Kuibyshev VD., B) on Valdai, g) in the Caspian Sea.

25. For the circulation of air, Antarctica is characteristic:

a) Passat, b) monsime, c) Stock winds, d) breeze.

26. Indicate the analogue of the flow of Gulf Stream in the Pacific:

a) Canary, b) Kurilsky, c) Kurosio, d) North-Pacific

27. The ice of the glacier is formed from

a) fresh water, b) sea water, c) atmospheric solid precipitation, d) atmospheric liquid precipitation.

Which travelers first reached the southern pole?

a) R.Chott, b) F. Bellinshausen, c) R.Amundsen, d) J.Kuk.

29. Place objects as they delete them from the audience where you are:

a) West Siberian Plain, b) Amazonian dilome., c) G. Kordillers, d) Sugar desert.

30. Find compliance:

Continent - Plant - Beast - Bird

Analytical Round (time per 100 min)

1. Explain why the globe is called the volume model of the Earth.

The globe almost completely repeats the formus of the Earth, the position of objects and its surface.

How does the form of the globe differ from the real form of the Earth?

Globus - a ball, the land is also surrounded by the poles.

2. Set which two hemispheres at the same time there is a boy depicted in this photo.

West and East

3. Determine what kind of coverage of territory includes the submitted maps. Using the Atlas, bring examples of cards of each type.

1 - Cards of countries (physical map of Russia).

2 - world maps (political map of the world, physical map of the world)

4. Place the parallels from the longest to the shortest.

45 ° Yu.Sh. 25 ° S.Sh., 0 ° sh., 70 ° Yu.Sh., 30 ° Yu.Sh. 60 ° C.SM 20 ° S.Sh.

0

20 S.Sh.

25 S.Sh.

30 S.Sh.

45 Yu.Sh.

60 S.Sh.

70 Yu.Sh.

5. In the picture, the ships of the Russian Antarctic Expedition "East" and "Mirny" are depicted at noon off the coast of Peter I (68 ° Yu.Sh.). Determine in which direction ships are moving.

In the southern hemisphere at noon, the sun bends to the north, as the ship floats towards the sun, he floats to the north.

6. Give examples of cards from your atlas, made in such ways that are shown in the drawings.

7. Determine in which parts of these cards the image of the Earth is distorted most. Explain why.

On the world map. Length is less than the equator. The smaller the scale, the greater the distortion.

8. Determine which from the figures depicted:

a) only parallels;

b) only meridians;

c) degree grid.

Date: 24.10.2015

Cartographic projection - Mathematical method of image of the globe (ellipsoid) on the plane.

For designing a spherical surface on the plane Used auxiliary surfaces.

By sight The auxiliary cartographic surface of the projection is divided into:

Cylindrical 1. (the auxiliary surface is the side surface of the cylinder), conical 2 (side surface of the cone), azimuthal 3. (The plane called picture).

Also highlight Polyconic

pseudo-cylindrical conditional

and other projections.

By orientation Auxiliary projection figures are divided into:

• normal (in which the axis of the cylinder or cone coincides with the axis of the Earth model, and the art plane is perpendicular to it);
• transverse (in which the axis of the cylinder or cone is perpendicular to the axis of the earth model, and the picture plane or parallel to it);
• obliquewhere the axis of the auxiliary figure is in an intermediate position between the pole and the equator.

Cartographic distortions - This is a violation of the geometric properties of the earth's surface objects (lengths of lines, corners, shapes and squares) when they are displayed on the map.

The smaller the scale of the card, the more distortion. On large-scale distortion maps is insignificant.

Select four types of distortion on maps: length, square, corners and form objects. Each projection is characterized by their distortion.

By the nature of distortion, cartographic projections are divided into:

• equifricularin which the corners and forms of objects are stored, but the lengths and square are distorted;

• isometricin which the area is stored, but the corners and forms of objects are substantially changed;

• arbitrary, in which distortion of lengths, squares and corners, but they are distributed on the map evenly. Among them, the rivopromizes of the projections are highlighted, in which there are no distortions of length or by parallel, or in meridians.

Lines and points of zero distortion - lines, along which and points in which there are no distortions, because here when designing a spherical surface to the plane, an auxiliary surface (cylinder, cone or picture plane) were tangent To the ball.

Scaleshown on the maps save only on lines and at points of zero distortion. It is called the main thing.

In all other parts of the map, the scale differs from the main thing and is called partial. It requires special calculations to determine.

To determine the character and magnitude of the distortion on the map, you need to compare the degree mesh of the map and the globe.

On globe All parallels are at the same distance from each other, everything meridians are equal to each other and intersect with parallels at right angles. Therefore, all the cells of the degree mesh between adjacent parallels have the same dimensions and shape, and the cells between the meridians are expanding and increase from the poles to the equator.

To determine the magnitude of the distortion, the ellipses of distortion are also analyzed - ellipseed figures formed as a result of distortion in a certain projection of circles conducted on the globe of the same scale as the map.

In an equally projection The ellipses of distortion have a circle form, the value of which increases depending on the distance from the points and the zero distortion lines.

In an isometric projection Ellipses of distortion have the form of ellipses whose areas are the same (the length of one axis increases, and the second is reduced).

In an equalization projection Ellipses of distortion have the form of ellipses with the same length of one of the axes.

Basic signs of distortion on the map

1. If the distance between the parallels is the same, this indicates that the distances in meridians are not distorted (equal exposure in meridians).
2. Distances are not distorted by parallel if the radii parallels on the map correspond to the radius parallels on the globe.
3. Square is not distorted if the cells created by meridians and parallels from the equator are squares, and their diagonals intersect at right angles.
4. The lengths of the parallel are distorted, if the lengths of the meridians are not distorted.
   
5. Distorted lengths in meridians, if the lengths are not distorted along the parallels.

The nature of the distortion in the main groups of cartographic projections

Cartographic projections	Distortions
Equifricular	Keep the corners, distort the area and length of lines.
Isometric	Keep areas, distort the angles and forms.
Equipment	In one direction there are a permanent scale of lengths, distortions of corners and areas are in equilibrium.
Arbitrary	Distort the corners and squares.
Cylindrical	There are no distortion along the equator line, and according to the degree of approach to poles - increase.
Conical	Distortion is missing along the cone and globe touch parenches.
Azimuth	Distortion is absent in the central part of the map.

Colombia is a country located in South America, bordering Panama, Peru, Ecuador, Venezuela and Brazil. Washed by the waters of the Pacific Ocean and the Caribbean.

Interactive maps

Convenient interactive map of Colombia, which can be moved and closer in the right place to obtain the necessary information. It can also be switched to satellite, relief and weather display mode.

Also, you can use another interactive map of Colombia adapted by Russian travelers.

Geographic map

The geographical map of Colombia, which shows the relief and natural features of the country, the main cities and roads, as well as borders with neighboring countries.

Educational and analytical information

Applying signs of distortion on maps, students set:

1. The map has a distortion of lines lengths, as the 20-degree segments of meridians increase from the center of the map and on the average meridian and to the side of it; On the parallels, there are also distortions of lengths (20-degree segments of parallels 60 ° C. w. near the average meridian is not twice as fewer than a 20-degree cut of the equator); Along the equator there is no distortion of lengths, its segments are equal. Conclusion: both meridians, and parallels, distorting, stretching with the removal from the central point of the map. Equator is not distorted.
2. The map has distortions of forms, since the forms of cartographic grid cells on one latitude (for example, along the equator) are different.
3. The map has distortion of the angles, which is clearly visible in many of its areas to deviate the angles of the intersection of meridians and parallels from 90 °.
4. The map has a distortion of space. It is visible to the eye to increase the area of \u200b\u200bthe cartographic grid cells to the edge of the map. For example, along the equator, the base of cells remain unchanged, and their heights are the greater, the closer the cell to the edge of the map. It follows from this that the cells of the cells grow in the same direction.

In the same way, distortions on the cards of hemispheres, mainland and the USSR can be analyzed. At the same time, the pattern is detected, that with a decrease in the coverage of the territory shown on the map is reduced, as a rule, the magnitude of the distortion. This conclusion can also be prompted by the teacher.

The general concept and determination of the cartographic projection is given in the textbook. Here, with sufficient completeness, three main types of projections are characterized, allocated according to the distortions inherent in it (equivalence, isometric and arbitrary), and the variety of arbitrary is equal - equalization.

A practically important task is to work out the skill on the basis of the analysis of the map of the map, to establish, to which of the names of the groups there is a projection in which this card is built. This conclusion must end the analysis of distortion on maps. The teacher needs to know affiliation to a particular group of card projections for their distortions. In arbitrary projections built: all world maps in the atlas for class VI, the map of North America on with. 4 in atlas for VII class; Arbitrary Equestrian Projection is represented by a global map in the same atlas.

Neither the program nor the textbook does not oblige seventh graders to study distortions on maps. But in the atlas for VII class, these indicators are depicted in the form of so-called distortion ellipses (in a graphical table with a mentioned "geometric representation of distortion"). This table shows how the form, the length of the radii and the area of \u200b\u200bthe geometric circle geometric circle are changed with the distance from the midpoint on the map, where it is not distorted. According to the top of the three drawings, it can be seen that in equally projections the form of the circle of IV changes, but its area grows; On the middle figure, it is proved that with the removal of the circle from an undischarged image, it turns into an ellipse with an area equal to the area of \u200b\u200bthe circle. The bottom drawing emphasizes how the shape and the area of \u200b\u200bthe initial circle increases. The following information may be useful to the teacher if students are interested in this pattern.

Differences (classification) of cartographic projections of training cards are shown in the atlas. On s. 4 Atlas for VII class There are drawings, explaining how to obtain projections cylindrical, conical and azimuth, applying as auxiliary surfaces according to the surface of the cylinder, cone or plane.

To clarify students to build cartographic projections using auxiliary geometric surface, it is useful at a lesson on this topic to use a geographic globe, a sheet of plywood or cardboard for an image of a plane and a sheet of drawing paper, which can be folded into a cylinder or cone. For example, explaining the receipt of a conical projection in which many Cards of the USSR are compiled, the teacher puts on a sheet of paper, rolled into the cone, to the globe so that the side surface of the cone comes into contact with the globe on one of the parallels, and the peak of the cone would be above the pole, on the continuation of the axis Rotation of Earth. Holding the cone in this position, the teacher outlines a soft pencil from the outside of the cone parallel touch, two or three other parallels and several meridians. At the same time, he says that when designing (transfer), the lines of the degree mesh on the surface of the cone parallel acquire the form of circles, and the meridians are direct directed to the top of the cone.

Having finished applying the lines of a degree grid on a paper cone, the teacher turns it into a plane and strengthens on the board so that students see the characteristic form of a cartographic grid in a conical projection. Of course, the mesh lines with such a drawing method cannot be even. You can draw them in advance on the opposite side of the paper and, attaching a sheet to the board, turn it with that side on which the grid was previously drawn. N. V. Malakhov recommends to link the study of the projection of cards with the projections of objects that students are used in the course of drawing. He writes: "Students, starting from the VII class, may mistakenly associate the projection of cards with a drawing course known to them from the course of parallel (orthogonal) projections, which are known to be obtained by designing items pa plane with parallel rays. The projections of the cards used at school have other design principles than in the draw.

In order for students to correctly understand cartographic projections, it is useful to compare the image of one of the hemispheres, for example, the eastern, on the map depicting the same hemisphere, but obtained according to the principle of orthogonal design. A similar image of the Eastern Hemisphere is used to show the Earth as planets and, in particular, in the Atlase for Teachers. "

Of course, the concepts of cartographic projections are formed particularly effectively by building a nart in different projections. For the lack of time in the lessons of geography, such work can be proposed by the participants of the school geographical circle or in the order of an individual independent task. How to build a cartographic grid in different projections, you can find out in the manual for teachers "Production of geographical maps in school."

Without such a consolidation of knowledge gained, the names of the projection groups and the information provided on their preparation of the geometric design on the auxiliary surface of one or another form, there is no disclosure of these concepts. In order for this information to be secured, it is necessary to record and remember the features of the distortion distribution in each group:

• in cylindrical projections, there are usually no distortion along the equator line, which is therefore a line of zero distortion. With the removal from the equator to the north and south of distortion grow;
• there are no distortions in the azimuth projection in the central point of the map. In all directions, they grow from this point of zero distortion.