The larger the scale of the map, the more detailed the depicted area. What is scale? Scale types
Each card has scale- a number that shows how many centimeters on the ground correspond to one centimeter on the map.
map scale usually listed on it. Record 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 on its terrain is 100,000,000 cm.
May be listed in numerical form as a fraction– numerical scale (for example, 1: 200,000). And it can be marked in linear form: as a simple line or strip divided into units of length (usually kilometers or miles).
The larger the scale of the map, the more detailed the elements of its content can be depicted on it, and vice versa, the smaller the scale, the more extensive space can be shown on the map sheet, but the terrain on it is depicted with less detail.
Scale is a fraction whose numerator is one. To determine which of the scales is larger and by how many times, let's recall the rule for comparing fractions with the same numerators: of two fractions with the same numerators, the one with the smaller denominator is larger.
The ratio of the distance on the map (in centimeters) to the corresponding distance on the ground (in centimeters) is equal to the scale of the map.
How does this knowledge help us in solving problems in mathematics?
Example 1
Let's look at two cards. A distance of 900 km between points A and B corresponds on one map to a distance of 3 cm. A distance of 1,500 km between points C and D corresponds to a distance of 5 cm on another map. Let us prove that the scales of the maps are the same.
Solution.
Find the scale of each map.
900 km = 90,000,000 cm;
the scale of the first map is: 3: 90,000,000 = 1: 30,000,000.
1500 km = 150,000,000 cm;
the scale of the second map is: 5: 150,000,000 = 1: 30,000,000.
Answer. The scales of the maps are the same, i.e. are equal to 1:30,000,000.
Example 2
The scale of the map is 1: 1,000,000. Let's find the distance between points A and B on the ground, if on the map
AB = 3.42 cm?
Solution.
Let's make an equation: the ratio of AB \u003d 3.42 cm on the map to the unknown distance x (in centimeters) is equal to the ratio between the same points A and B on the ground to the map scale:
3.42: x = 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
The scale of the map is 1: 1,000,000. The distance between points on the ground is 38.4 km. What is the distance between these points on the map?
Solution.
The ratio of the unknown distance x 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 map.
38.4 km = 3,840,000 cm;
x: 3,840,000 = 1: 1,000,000;
x \u003d 3,840,000 1: 1,000,000 \u003d 3.84.
Answer: the distance between points A and B on the map is 3.84 cm.
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The scale is the ratio of the real dimensions of the object to the image, the model of the object.
The geographical scale helps to determine how many times on the map all real sizes have been reduced - the area of \u200b\u200bthe territory, individual objects, the length of rivers, roads, etc.
In ancient times, the scale was not known, because the objects were placed on the map at an arbitrary distance from each other. Using such a map, a person could not determine whether he would get to the right place in 2 days, 2 weeks or 2 months.
The first cartographer to use a scale in mapping was Anaximander of Miletus, an ancient Greek scientist (VI-V centuries BC), who coined the term "law" and proposed the first formulation of the conservation law.
Depending on the scale, maps are conditionally divided into:
- small-scale (survey) - less than 1: 1,000,000;
- medium-scale (survey-topographic) - from 1:200,000 to 1:1,000,000;
- large-scale (topographic) - from 1:10,000 to 1:100,000.
Scales up to 1:5,000 are mainly used in drawing up a topographic plan.
Scale type: graphic, numerical, named scales
In the legends of geographical maps, they use a graphic (it is also linear) and a numerical scale, they rarely resort to a named one.
Scale numerical
Fractions are used to write it, in which the numerators are 1 cm (unless otherwise specified), and the denominators are numbers showing how many times the indicator is reduced. For example, a scale of 1:25,000 shows that 1 cm of the map corresponds to 25,000 cm (250 m) of terrain.
The smaller the denominator, the larger the scale: 1:1000 is larger than 1:5000, because in the first case, 10 m “fits” in 1 cm of the map, and 50 m in the second. Maps with a large scale are more detailed, more meaningful, but they can be used for small areas of the area.
Linear (graphical) scale
The linear or graphical scale is especially convenient and makes it possible to find out distances, sizes without calculations and transferring lengths from scale to real. The linear scale looks like a ruler with divisions - small and large, each of which is signed by the corresponding metric value. The major division is usually a 2cm segment for which a scale size is specified, such as 100m, 500m, etc. 
To use the graphic scale, a compass solution equal to the measured segment is applied to the scale ruler and they immediately find out the distance between objects, the length of the desired section, etc.
Named Scale
The named scale differs from others in that it says in words how many meters or kilometers are contained in 1 cm. For example: in 1 cm - 250 m; in 1 cm - 5 km.
Where to find the scale on the map?
To find out the scale of a geographical map, you need to look at the corners of the map or its legend. A legend is a list of symbols with their explanation.
Very often, all 3 types of scales are shown on the maps, so that each person can figure out how many times the real distances are reduced on the map.
Numerical Scale Standards
The Russian Federation has adopted the following numerical scale standards:
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 maps with a scale of 1:2,000, 1:5,000. They are used for special tasks, because such large scales are the scope of topographic plans.
There are survey maps with an incredibly small scale, for example - 1:1,000,000,000 (one in a trillion). It was created in 2010 by scientists at the University of Ghent in Belgium, using CMOS semiconductor fabrication technology. on this map is 40 micrometers long - 0.04 mm, about half the thickness of a human hair. 
And the "Map of the Industrialization of the USSR" from the St. Petersburg Geological Prospecting Museum is famous not only for its huge scale - 1: 1,500,000, but also ... for its beauty. It was made for the 20th anniversary of the October Revolution in 1937 from 50,000 fragments, including Ural jasper for land, lapis lazuli for water, and amazonite for lowlands. The map is 6 m long, 4.5 m high, and weighs about 3.5 tons. At the World Exhibition in Paris in 1937, the map was awarded the Grand Prix, and in New York - a gold medal.
To depict the Earth's surface on maps, cartographers had to solve a mathematical problem. It was necessary to reduce the image and determine which objects, with a particular reduction, can be shown on.
Why is scale needed?
On old maps and plans, the real area is shown in a reduced form. But different areas are reduced in different ways. Therefore, according to old maps, you can determine the outlines of objects, but not their sizes. To measure the length of a river or the distance between cities, it is required to reduce the image of the area and all objects by a certain number of times. To do this, you need to use a scale.
Scale is the ratio of two numbers, such as 1:100 or 1:1000. The ratio shows how many times one number is greater than another. A scale of 1:100 means that the image is one hundred times smaller than the depicted object, and a scale of 1:1000 means that it is a thousand times smaller. The smaller the number indicating the decrease, the larger the scale, and vice versa. Scale 1:100 is larger than scale 1:1000 and smaller than scale 1:50.
Linear scale- a line divided into centimeter segments. The segments to the right of zero show what distance on the ground corresponds to 1 centimeter on a plan or map. The segment to the left of zero is divided into five smaller parts for greater measurement accuracy. By measuring the distance between objects using a measuring compass, you can apply it to a linear scale and get distances on the ground. Using a linear scale, determine the length of curved lines (coastline of the sea, river or road).
Image scale and details
Depending on the scale, the degree of detail of the image changes. The larger the scale, the more detailed the parts of the Earth with all geographical objects are depicted. But on large-scale images (1:200,000 and larger), only a small area of the earth's surface fits. On small-scale maps (smaller than 1:1000,000), where 1 centimeter corresponds to several thousand kilometers on the ground, even the entire surface of the Earth can be shown. However, the amount of detail and terrain detail here is low.
Often, for educational and practical purposes, it is necessary to create plans and maps of varying degrees of detail and, therefore, scale.
Without it, it is impossible to build any geographical map. What is scale? And what types of scales exist in cartography and geodesy? This will be discussed in this article.
What is scale?
Scale is a German word (masstab), which consists of two parts: mass - "measure, size" and stab - "stick, pole". Measuring pole - that's how you can translate this term.
What is scale? In the general interpretation, this is a mathematical value that shows how many times the model (image) is reduced in comparison with the original. This concept is actively used in mathematics, cartography, modeling, geodesy and design, photography, and programming.
In other words, scale is the ratio of two linear dimensions. In cartography, it shows how many times a segment on a map (or plan) is reduced compared to the actual length of the same segment. When compiling any geographical map, it is impossible to depict objects (forest, village, building, etc.) in real size. Therefore, all values are repeatedly reduced (by 5, 10, 100, 1000 times, and so on). The scale of the map is precisely this value, expressed as a number.
Scale types
The scale is shown on maps and drawings using numbers or graphically. Accordingly, there are several types of them.
The numerical scale looks like a fraction. It is most common in cartography. Many of us have seen such a designation at the bottom of a topographic map or terrain plan. The numerical scale of the map has the following form (for example): 1:100,000. This means that the actual length of the segment on the ground is 100,000 times greater than its length on the given map.
A named scale is used when you need to know what the map scale is. It is also quite often indicated on geographical maps. It looks like this: 1 cm - 1 km.
Linear scale is already a graphic type of scale. It is a ruler, which is divided into graphs of the corresponding sizes. The photo above shows this type of scale.
The transverse scale is a more sophisticated version of the graphical view. It is used for the most accurate measurements, and it can be found on more serious maps.
How to use the map scale correctly? Suppose you need to find out on a specific map the real distance between villages A and B. At the same time, you are given the following scale: 1 cm - 0.5 km (or 1:50,000). To do this, you need to take a regular ruler and measure the distance between two points on the map. Then the resulting value (suppose it is a segment 5 centimeters long) should be multiplied by 0.5 km, according to the scale of our map. Thus, we will get the correct answer: the distance between village A and village B is 2.5 kilometers.
Varieties of maps (by scale)
The scale is one of the criteria for the classification of geographical 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 and more).
Of course, on large-scale maps, the terrain is more detailed: individual streets or even buildings can be shown here. The larger the scale of the map, the more terrain objects can be depicted on it.
Small-scale geographical maps, as a rule, are used to depict hemispheres and continents, medium-scale maps - for states and their parts, large-scale maps - for individual, small territories. The military, local historians, as well as tourists are very familiar with large-scale maps.
Cartographic generalization
No matter how detailed the map is, it still cannot display absolutely all the objects and details that are present in the area. This is precisely 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 features that will be depicted on a particular map. Moreover, this process is objective, expedient and scientifically substantiated.
To understand what generalization is, it is enough to recall the cards that you probably held 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 Oblast, it will definitely be marked.
Cartographic generalization helps to make the map as high quality and functional as possible, easy to read. Of course, it directly depends on the scale.
Finally
So what is scale? This value shows how reduced the image is compared to the actual size of the depicted object. This concept is most widely used in cartography and geography. There are several types of scales: numerical, named, linear and transverse.
The concept of cartographic generalization is closely related to the term "scale". This process allows topographers to select the most important geographic features and display them on a geographic map.
Each card has scale- a number that shows how many centimeters on the ground correspond to one centimeter on the map.
map scale usually listed on it. Record 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 on its terrain is 100,000,000 cm.
May be listed in numerical form as a fraction– numerical scale (for example, 1: 200,000). And it can be marked in linear form: as a simple line or strip divided into units of length (usually kilometers or miles).
The larger the scale of the map, the more detailed the elements of its content can be depicted on it, and vice versa, the smaller the scale, the more extensive space can be shown on the map sheet, but the terrain on it is depicted with less detail.
Scale is a fraction whose numerator is one. To determine which of the scales is larger and by how many times, let's recall the rule for comparing fractions with the same numerators: of two fractions with the same numerators, the one with the smaller denominator is larger.
The ratio of the distance on the map (in centimeters) to the corresponding distance on the ground (in centimeters) is equal to the scale of the map.
How does this knowledge help us in solving problems in mathematics?
Example 1
Let's look at two cards. A distance of 900 km between points A and B corresponds on one map to a distance of 3 cm. A distance of 1,500 km between points C and D corresponds to a distance of 5 cm on another map. Let us prove that the scales of the maps are the same.
Solution.
Find the scale of each map.
900 km = 90,000,000 cm;
the scale of the first map is: 3: 90,000,000 = 1: 30,000,000.
1500 km = 150,000,000 cm;
the scale of the second map is: 5: 150,000,000 = 1: 30,000,000.
Answer. The scales of the maps are the same, i.e. are equal to 1:30,000,000.
Example 2
The scale of the map is 1: 1,000,000. Let's find the distance between points A and B on the ground, if on the map
AB = 3.42 cm?
Solution.
Let's make an equation: the ratio of AB \u003d 3.42 cm on the map to the unknown distance x (in centimeters) is equal to the ratio between the same points A and B on the ground to the map scale:
3.42: x = 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
The scale of the map is 1: 1,000,000. The distance between points on the ground is 38.4 km. What is the distance between these points on the map?
Solution.
The ratio of the unknown distance x 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 map.
38.4 km = 3,840,000 cm;
x: 3,840,000 = 1: 1,000,000;
x \u003d 3,840,000 1: 1,000,000 \u003d 3.84.
Answer: the distance between points A and B on the map is 3.84 cm.
Do you have any questions? Don't know how to solve problems?
To get the help of a tutor - register.
The first lesson is free!
site, with full or partial copying of the material, a link to the source is required.