The larger the scale of the card the greater. What is the scale of the card in geography? What is scale
Scale call the ratio of the present sizes of the object to the image, the model of the object.
The geographical scale helps determine how many times on the map all real dimensions were reduced - the area of \u200b\u200bthe territory, individual objects, the length of rivers, roads, etc.
In antiquity, the scale did not know, because the objects had on the map at an arbitrary distance from each other. Using such a card, a person could not determine whether he would get to the right place 2 days, 2 weeks or 2 months.
The first cartographer applied to the scale of the map was Anaximandr Miretsky - an ancient Greek scientist (VI - V centuries. BC), who invented the term "law" and proposed the first wording of the conservation law.
Depending on the scale of the map conventionally divided into:
- small-scale (review) - less than 1: 1 000 000;
- Medium-scale (topographic surveillance) - from 1: 200,000 to 1: 1 000 000;
- Large-scale (topographic) - from 1:10,000 to 1: 100 000.
Scale up to 1: 5,000 are used mainly in the preparation of the topographic plan.
Scale view: scales graphic, numerical, named
In the legends of geographic maps, graphic (it is also linear) and numerical scale are rarely resorted to the named one.
Numerical scale
For its record, a fraction is used in which numerals are 1 cm (unless otherwise specified), and the denominators - numbers showing which time the indicator is reduced. For example, scale 1:25 000 demonstrates that 1 cm card corresponds to 25,000 cm (250 m) of the area.
The smaller the denominator, the larger scale: 1: 1000 larger than 1: 5,000, because In the first case, a 1 cm card "fits" 10 m, and in the second - 50 m. Maps with a large scale more, more substantially, but it is possible to use them for small areas of the terrain.
Linear (graphic) scale
Linear, or graphic scale, especially convenient and allows you to learn distances, dimensions without calculation and translations of lengthy lengths in real. A linear scale looks like a line with divisions - small and large, each of which signed by the corresponding metric value. The main division is usually a segment of 2 cm, for which the size of scaling is indicated, for example - 100 m, 500 m, etc. 
To take advantage of the graphic scale, the circulation solution equal to the measured segment is applied to the scale line and immediately recognize the distance between objects, the length of the desired site, etc.
Named scale
A named scale is different from others in that it is written in words how many in 1 cm contains meters or kilometers. For example: 1 cm - 250 m; 1 cm - 5 km.
Where to look for scale on the map?
To find out the scale of the geographic map, you need to see the corners of the card or its legend. The legend call a list of designations with their clarification.
Very often, all 3 types of scale are given on the maps, so that each person can figure out how many times the real distances are reduced on the map.
Standards of numerical scales
IN Russian Federation The following numerical scale standards are taken:
1:10 000
1:25 000
1:50 000
1:100 000
1:200 000
1:300 000
1:500 000
1:1 000 000
There are also cards with a scale of 1: 2,000, 1: 5,000. They are used for special tasks, because Such large scale - scope topographic plans.
There are reviews geographic Maps With incredibly small scale, for example - 1: 1 000 000 000 (one to the trillion). It was created in 2010, the scientists of the Gent University in Belgium, using the CMOS semiconductor manufacturing technology. This map has a length of 40 micrometers - 0.04 mm, about half of the thickness of the human hair. 
And the "USSR Industrialization Map" from the St. Petersburg geological exploration museum is famous not only with its huge scale - 1: 1,500,000, but also ... beauty. It was manufactured for the 20th anniversary of the October Revolution in 1937 of 50,000 fragments, among which - the Ural Jasper for Sushi, lazuli - for water, amazonite - for lowlands. The length of the card is 6 m, the height is 4.5 m, the weight is about 3.5 tons. At the World Paris Exhibition of 1937, the map was awarded the Grand Prix, and in New York - the Golden Medal.
Each card has scale- The number that shows how many centimeters on the ground corresponds to one centimeter on the map.
Map scale Usually indicated on it. Recording 1: 100 000 000 means that if the distance between two points on the map is 1 cm, then the distance between the corresponding points of its locality is 100,000,000 cm.
Can be specified in numerical form in the form of a fraction - Numerical scale (for example, 1: 200,000). And can be marked linear form: In the form of a simple line or strip, divided by units of length (usually per kilometers or miles).
The larger the scale of the card, the items of its content can be depicted with more detail, and vice versa, the smaller the scale, the more extensive space can be shown on the card sheet, but the terrain on it is depicted with less details.
Scale is a fraction, In the numerator of which one. To determine which of the scale is larger and how many times, we will recall the comparison of fractions with the same numerals: from two fractions with the same numerators more that less denominator.
The distance of the distance on the map (in centimeters) to the corresponding distance on the ground (in centimeters) is equal to the map scale.
How will these knowledge help us when solving problems in mathematics?
Example 1.
Consider two cards. The distance to 900 km between points A and B corresponds to on the same map of 3 cm. The distance in 1,500 km between points C and D corresponds to another map of 5 cm. We prove that the scale of the cards are the same.
Decision.
Find the scale of each card.
900 km \u003d 90 000 000 cm;
the scale of the first card is: 3: 90 000 000 \u003d 1: 30 000 000.
1500 km \u003d 150 000 000 cm;
the scale of the second card is: 5: 150 000 000 \u003d 1: 30 000 000.
Answer. The scale of the cards is the same, i.e. equal to 1: 30 000 000.
Example 2.
Card scale - 1: 1 000 000. Find the distance between points A and B on the ground if on the map
AB \u003d 3.42. cm?
Decision.
We will make an equation: the ratio of AB \u003d 3.42 cm on the map to the distance unknown to us (in centimeters) is equal to the ratio between the same points A and in the area to the scale of the card:
3.42: x \u003d 1: 1 000 000;
x · 1 \u003d 3.42 · 1 000 000;
x \u003d 3 420 000 cm \u003d 34.2 km.
Answer: The distance between points A and B on the ground is 34.2 km.
Example 3.
Card scale - 1: 1 000 000. The distance between points on the area is 38.4 km. What is the distance between these items on the map?
Decision.
The attitude of the distance of the distance from us between points A and B on the map to the distance in centimeters between the same points A and B on the ground is equal to the scale of the card.
38.4 km \u003d 3,840,000 cm;
x: 3 840 000 \u003d 1: 1 000 000;
x \u003d 3 840 000 · 1: 1 000 000 \u003d 3.84.
Answer: The distance between points A and on the map is 3.84 cm.
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Each card has scale- The number that shows how many centimeters on the ground corresponds to one centimeter on the map.
Map scale Usually indicated on it. Recording 1: 100 000 000 means that if the distance between two points on the map is 1 cm, then the distance between the corresponding points of its locality is 100,000,000 cm.
Can be specified in numerical form in the form of a fraction - Numerical scale (for example, 1: 200,000). And can be marked linear form: In the form of a simple line or strip, divided by units of length (usually per kilometers or miles).
The larger the scale of the card, the items of its content can be depicted with more detail, and vice versa, the smaller the scale, the more extensive space can be shown on the card sheet, but the terrain on it is depicted with less details.
Scale is a fraction, In the numerator of which one. To determine which of the scale is larger and how many times, we will recall the comparison of fractions with the same numerals: from two fractions with the same numerators more that less denominator.
The distance of the distance on the map (in centimeters) to the corresponding distance on the ground (in centimeters) is equal to the map scale.
How will these knowledge help us when solving problems in mathematics?
Example 1.
Consider two cards. The distance to 900 km between points A and B corresponds to on the same map of 3 cm. The distance in 1,500 km between points C and D corresponds to another map of 5 cm. We prove that the scale of the cards are the same.
Decision.
Find the scale of each card.
900 km \u003d 90 000 000 cm;
the scale of the first card is: 3: 90 000 000 \u003d 1: 30 000 000.
1500 km \u003d 150 000 000 cm;
the scale of the second card is: 5: 150 000 000 \u003d 1: 30 000 000.
Answer. The scale of the cards is the same, i.e. equal to 1: 30 000 000.
Example 2.
Card scale - 1: 1 000 000. Find the distance between points A and B on the ground if on the map
AB \u003d 3.42. cm?
Decision.
We will make an equation: the ratio of AB \u003d 3.42 cm on the map to the distance unknown to us (in centimeters) is equal to the ratio between the same points A and in the area to the scale of the card:
3.42: x \u003d 1: 1 000 000;
x · 1 \u003d 3.42 · 1 000 000;
x \u003d 3 420 000 cm \u003d 34.2 km.
Answer: The distance between points A and B on the ground is 34.2 km.
Example 3.
Card scale - 1: 1 000 000. The distance between points on the area is 38.4 km. What is the distance between these items on the map?
Decision.
The attitude of the distance of the distance from us between points A and B on the map to the distance in centimeters between the same points A and B on the ground is equal to the scale of the card.
38.4 km \u003d 3,840,000 cm;
x: 3 840 000 \u003d 1: 1 000 000;
x \u003d 3 840 000 · 1: 1 000 000 \u003d 3.84.
Answer: The distance between points A and on the map is 3.84 cm.
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For the image of the surface of the Earth on the maps of cardographic, the mathematical task was to solve. It was necessary to reduce the image and determine which objects with one or another reduction can be shown on.
Why do you need a scale?
On the ancient maps and plans, the real area is shown in a reduced form. But different sections are reduced in different ways. Therefore, in old cards You can define the outlines of objects, but not their dimensions. To measure the length of the river or the distance between cities, it is required to reduce the image of the area and all objects in a certain number of times. To do this, use the scale.
Scale is the ratio of two numbers, for example 1: 100 or 1: 1000. The attitude shows how many times one number more than the other. Scale 1: 100 means that the image is smaller than the displayed object at a hundred times, and the scale of 1: 1000 is a thousand times. The smaller the number indicating the decrease, the larger the scale, and vice versa. Scale 1: 100 Larger scale 1: 1000 and smaller scale 1:50.
Linear scale - Line separated by centimeter segments. Segments to the right of zero show, what area on the ground corresponds to 1 centimeter on the plan or map. The segment to the left of zero for greater accuracy of measurements is divided into five smaller parts. Measuring the distance between objects using a circulator, you can apply it to a linear scale and receive distances on the ground. Using a linear scale, determine the length of the lines (coastline of the sea, river or road).
Scale and details of the image
Depending on the scale, the degree of details of the image is changing. The larger the scale, the details are depicted areas of land with all geographic objects. But on image of a large scale (1: 200,000 and larger) only a small area ground surface. On small-scale maps (smaller 1: 1000,000), where 1 centimeter corresponds to several thousand kilometers on the ground, it is possible to show even the entire surface of the earth. However, the number of parts and details of the area is small here.
Often, educational and practical purposes have to create plans and maps of varying degrees of detail and, therefore, scale.
Without it, it is impossible to build a single geographic map. What is the scale? And what types of scales exist in cartography and geodesy? This will be discussed in this article.
What is the scale?
Scale is the word German (masstab), which consists of two parts: Mass - "Measure, the magnitude" and Stab - "stick, pole". The measuring pole is how this term can be translated.
What is the scale? In general interpretation, this is a mathematical value that shows how many times the model (image) is reduced compared to the original. This concept is actively used in mathematics, cartography, models, geodesy and design, photo art, programming.
In other words, the scale is the ratio of two linear sizes. In cartography, it shows how many times the segment on the map (or plan) is reduced compared to the real length of the same segment. In the preparation of any geographical map, it is impossible to depict objects (forest, village, building, etc.) into a real amount. Therefore, all values \u200b\u200bare repeatedly reduced (at 5, 10, 100, 1000 times and so on). The scale of the card is just a given value, expressed by the number.
Species of scale
Scale is shown on maps and drawings with numbers or graphically. Accordingly, several of their species stand out.
Numerical scale has the form of a fraction. It is most common in cartography. Such a designation Many of us have seen at the bottom topographic map or terrain plan. The numerical scale of the card has the following form (for example): 1: 100 000. This means that the real length of the segment is 100,000 times larger than its length on this card.
A named scale is used when it is necessary to know what is equal to the scale of the card. It is also fairly often indicated on geographic maps. It has this kind: 1 cm - 1 km.
Linear scale is already a graphic type of scale. It is a ruler that is divided into columns of the corresponding sizes. The photo above shows this type of scale.
A transverse scale is a more complicated option. graphic view. It is used for the most accurate measurements, and it can be found on more serious maps.
How to use the scale of the map? Suppose you need to find out the real distance between the villages A and B. This is given to you this scale: 1 cm is 0.5 km (or 1:50,000). To do this, take the usual ruler and measure the distance between the two points on the map. Then the value obtained (suppose it is a length of 5 centimeters long) should be multiplied by 0.5 km, respectively, the scale of our card. Thus, we will get the right answer: the distance between Selo A and the village of is 2.5 kilometers.
Varieties of cards (on-scale)
The scale is one of the criteria for the classification of geographic maps. So, according to him, all cards are divided into:
- small-scale (scale up to 1: 1 000 000);
- medium-scale (from 1: 1 000 000 to 1: 200,000);
- large-scale (from 1: 200,000 or more).
Of course, the terrain is more detailed on large-scale maps: individual streets or even buildings can be shown here. The larger the scale of the card, the more object objects on it can be depicted.
Small-scale geographical maps are usually used for the image of hemispheres and continents, the range - for states and their parts, large-scale - for individual, small areas of the territories. With large-scale maps, military, local history, as well as tourists are very familiar.
Cartographic generalization
Whatever detailed a card, it still will not be able to display absolutely all objects and parts that are present on this locality. This is exactly the essence of the concept of "cartographic generalization".
The word generalis can be translated from Latin as "generalized". Generalization is the process of selecting those geographic objectswhich will be depicted on a specific map. Moreover, this process is objective, appropriate and scientifically justified.
To understand what kind of generalization is enough to recall those cards that you probably kept in your hands. So, on the map of Eurasia you are unlikely to find the city of Cherepovets. But on the map of the Vologda region, it will definitely be marked.
Cartographic generalization helps to make a map as high quality and functional, easily readable. Of course, it directly depends on the scale.
Finally
So what is the scale? This value shows how reduced the image is compared to real dimensions The object is depicted. This concept was obtained the greatest distribution in cartography and geography. There are several types of scale: numerical, named, linear and transverse.
The term "scale" is closely associated with the concept of cartographic generalization. This process allows topographs to select the most important geographical objects and display them on the geographic map.