Despite the fact that our planet is a relatively temperate place in terms of climate and geographic data, there are places on it that will amaze you with their level of extreme, be it the coldest place on Earth or the deepest trench in the ocean. Get ready for these 25 locations to surprise you with their fantastic performance!

Hottest inhabited place - Dallol, Ethiopia

The average daily temperature is 34.4 degrees Celsius.

The deepest cave - Krubera-Voronya cave

It is located in Abkhazia, the depth is more than 2000 m.

Highest point - Mount Everest

The height of the mountain is 8 848 m above sea level.

Farthest point from the center of the Earth - Chimborazo, Ecuador

The most remote island - Bouvet island

The Norwegian island in the South Atlantic Ocean is located 1000 miles from Antarctica and almost 1500 miles from South Africa.

The most distant continental point is the Antarctic Pole of Inaccessibility

It is the farthest point on the continent from any ocean. And Antarctica is the most remote continent.

Flattest place - Salar de Uyuni, Bolivia

The world's largest salt marsh with an area of ​​4086 sq. miles.

Highest navigable lake - Titicaca

The lake on the border with Bolivia is located at an altitude of 3812 m.

The lowest point on land is the Dead Sea coast

This point separates Jordan and the West Bank at 418 m below sea level.

Longest mountain range - Andes, South America

The ridge is 5,000 miles long and runs through 7 countries in South America.

The deepest man-made hole - Kola superdeep well

Its depth reaches 12,262 m.

Rainiest Place - Choco, Colombia

It receives 11,770 cm of precipitation per year.

Driest place - Atacama Desert, Chile

Most populous landlocked country - Ethiopia

70 million people have no access to the coastline.

Largest elevation difference - Mount Thor, Canada

Altitude 1250 m, average angle 105 degrees.

Coldest settlement - Oymyakon, Russia

For 7 months of the year, temperatures are kept well below zero.

Windiest place - Commonwealth Bay, Antarctica

Winds regularly exceed 240 km / h, and the average annual wind speed is 80 km / h.

Highest Falls - Angel, Venezuela

Its height reaches 1054 m, and the water has time to evaporate before it reaches the ground.

Highest mountain pass - Marsimik-La, India

Located at an altitude of 5582 m.

The largest freshwater lake - Lake Superior

Its area is 31,820 sq. miles.

Country with longest coastline - Canada

The coastline stretches for 151,019 miles.

Largest Gorge - Grand Canyon, USA

It is nearly 220 miles long and about a mile deep.

Largest Glacier - Lambert-Fischer, Antarctica

Stretches over 100 miles.

Shortest river - Rowe, Montana

Its length is only 61 m.

Lowest point - Challenger Abyss

Located in the lower part of the Mariana Trench at a depth of 10,911 m below sea level.

Coastline length

Is it measurable?
Do we have the right to give the length in textbooks
coastline and don't we get embarrassed,
asking this figure from the students?

K.S. LAZAREVICH

In geography lessons, we operate with many statistical indicators. Most of them look very simple and clear: so many millions of people, so many million tons of coal, so many kilometers. But this is if you do not ponder. And one has only to dig deeper into any number - and it ceases to be clear. Sometimes it crumbles to dust. Here are some examples.
We open the recently published and just put on sale Atlas of the world (Moscow: FGUP Production mapping association "Cartography", 2003.). In the table "States and territories of the world" we find: "The capital of France is Paris (2 125.2 thousand inhabitants). If a student gives such a figure on the exam, will the examiner be satisfied? After all, Paris is one of the largest centers in Europe and no less than Petersburg. But there is no mistake in the given figure: this is Paris within the administrative boundaries of the city of Paris. And within the boundaries of a really formed urban cluster - this is a ten-millionaire. Much depends on how you count. This does not mean that we can accept from the student as an answer any number in the range from 2.2 to 10; citing this or that number, the student must understand what stands behind it, what is measured and how.
Million tons of high-calorific coal and brown coal - different millions.
But here, it would seem, kilometers. A kilometer is a kilometer in Africa. And what can be questioned, measured in kilometers? But, it turns out, and giving the lengths in kilometers, the author of the textbook must first think. The teacher, using the textbook, must also subject the figure to critical analysis before broadcasting it to the students and demanding memorization. We read a textbook for the 10th grade: "Canada goes to three oceans, and the total length of its coastline (about 250 thousand km) is unmatched in the world." How was the coastline measured, what was measured, how was it measured, what was it measured? How can a coastline be measured at all?

Incorrect curves on the map can be measured with a curvimeter - the wheel of this device is rolled along a curve, carefully writing out each gyrus. However, the tortuosity of the coastline is often so great that it is impossible to walk along it with a curvimeter. You have to step along the curve with a pair of calipers. The most convenient step length is 2 mm. On different scales, this step corresponds, of course, to different distances, such a measurement will never give an exact length, since each step straightens the curve over a small segment, but the relative error is more or less preserved.
Let's, for the sake of example, try to measure the length of the coastline of the Chukotka Autonomous Okrug. Let's take a map from the School atlas on the geography of Russia (scale 1: 22,000,000) and walk the entire Chukchi coast with a two-millimeter step of a compass (44 km). The result will be 4300 km (98 steps of the compass). Let's make the same measurement on the scale map
1: 7,500,000. Here we already count 345 two-millimeter (15 km) steps, that is
5 200 km. It is logical to assume that if a map of an even larger scale is used in the measurements, the measured coastline will become even longer.
Let's try another experiment. The length of the coastline of the Leningrad region. on the map
1: 22,000,000 - 300 km, on a map 1: 2,500,000 - 555 km, and on a topographic map
1: 500,000 - 670 km. At the same time, the length of the coastline of the Vyborg Bay alone (where the shores are especially indented by bays and coves), measured according to the topographic map, is 338 km, while according to the school atlas - 65 km (the difference is more than
Five times!).
Thus, there is a regular increase in the length of the measured coastline with the enlargement of the scale. The reason is not only that the two-millimeter step of the compass corresponds to an ever-smaller value on the ground, but mainly because the line itself, even if it is very accurately measured and translated in accordance with the scale in kilometers, actually becomes longer (Fig. 1) ... On the map of Russia off the coast of the Leningrad region. only the Vyborg Bay, the Neva Bay and small bends of the southern coast of the Gulf of Finland are guessed. On a map with a scale of 1: 2,500,000, the outlines of the Vyborg Bay are already quite complex, and in the south the Koporskaya and Luga bays are clearly visible. On a half-million map within the Vyborg Bay, there are many other small bays, some of which have their own names (Baltiets Bay, Klyuchevskaya Bay), and only the southern coast of the Gulf of Finland looks little changed compared to the previous scale, where the coast is much less indented.

How do you determine the exact length of the coastline?
This goal was set by the English meteorologist Richardson, choosing his home island - Great Britain as a testing ground. He came to the conclusion about an increase in the length of the coastline with an increase in the scale of the map, according to which this length is measured (Fig. 2). Is there a limit to this increase? Hardly. The length of the coastline is increased by each small sand spit jutting into the sea, each hollow that creates a tiny bay, each pebble that flows around the water. Even on the most large-scale map they are not visible, meanwhile, in reality, all these irregularities of the coastline exist.

Many examples are given of how the use of mathematical methods can make geographical research more convincing, more reliable. Here, the opposite happened: geographical research - the study of the length of the coastline - contributed to the emergence of a new mathematical concept. The English name for this concept is fractal, in Russian it has not yet finally settled down and is found in three versions: fractal(genitive and instrumental cases will be fractal, fractal), fractal masculine ( fractal, fractal) and fractal feminine ( fractals, fractal); lately seems to be leaning towards fractal.
A fractal is a line, each fragment of which becomes infinitely more complicated, the length of each fragment and the entire line is constantly increasing. An example is the figure usually called the Koch snowflake, although the name is incorrect: she built this snowflake at the beginning of the 20th century. Helga von Koch, and her name should not be declined.
Take an equilateral triangle. Let's divide each of its sides into three equal parts and build an equilateral triangle on the middle segment of each side. You will get a regular six-pointed star, a figure with six convex corners and six incoming ones. We divide each of its sides (and there are 12 of these sides) into three equal parts and on the middle segment of each side we again construct an equilateral triangle. You will get a figure with 48 sides, with 18 convex and 30 incoming corners. Repeating this operation an infinite number of times (this can be done, of course, only mentally), we get a figure whose area is constantly increasing, but more and more slowly, gradually approaching a certain limit (Fig. 3). The perimeter of this figure increases infinitely, since every time we build a new equilateral triangle on the side of the figure, no matter how small it is, three equal segments of this side are replaced by four of the same and therefore the length of each side (and therefore the entire perimeter) increases by 4/3 times, and any number greater than one to a degree equal to infinity (and we do the construction an infinite number of times) tends to infinity.

The border of the snowflake will be something like a wide, shaggy line that fills the entire border area of ​​this figure. The concepts of "wide line", "thick surface", seemingly absurd from the point of view of classical mathematics (the line there has no width, and the surface has no thickness), with the development of the theory of fractals acquired the rights of citizenship. It is considered that the line is one-dimensional, it has only length, the position of a point on it is determined by one coordinate; the surface is two-dimensional, it has an area, the position of a point on it is determined by two coordinates; the body is three-dimensional, it has volume, three coordinates are needed. And the theory of fractals introduces the concept of fractional dimension: the line has not become two-dimensional, but has ceased to be one-dimensional. For an untrained person, this is quite difficult to understand (you can't sneeze one and a half times), but if we remember how the coastline behaves - not only on the map, but also in nature, how it changes if you look at it, squatting down, then straightening up full height, then climbing a mountain, then taking off in an airplane or spaceship, we will not so much understand, but feel what a complex system this line represents; for her, one characteristic is definitely not enough - length.
And the theory of fractals, born of geographical research, itself comes to the aid of geography. The method of studying relief as a fractal has not been developed yet, but it definitely has prospects. Considering the relief in general, drawing it on a small-scale map, we see mountain ranges, plateaus, deep valleys. On an average scale, hills, small valleys, and ravines are already looming. Even larger - and bumps are visible, wind ripples in the sand. But this is not the limit: there are individual pebbles, grains of sand. In practical terms, all this is important because you need to learn how to correctly select objects for images on maps of different scales; one of the main mistakes of the map compilers is the discrepancy between the content of the map and its scale, the map is either underloaded or overloaded.
But what to do with the length of the coastline? Refuse to measure it because it is immeasurable?
No, this is not an option. Simply, giving the length of the coastline, you should always indicate on what scale maps it was measured in what way. And be sure to stipulate at the same time, whether the coastline of the islands was taken into account or not. Without specifying the scale of the maps and whether the islands are taken into account or not, any data on the length of the coastline becomes meaningless. Unfortunately, even in sources that claim to be especially solid, one can find terrible absurdities. For example, the famous CIA website "The World Factbook". Here coastline data is shown for each country and ocean, but no measurement method is specified. As a result, the coastline of Canada is more than 200 thousand km, the Arctic Ocean - 45.4 thousand km, the Atlantic - 111.9 thousand km (the data is given - don't think bad! - with an accuracy of a kilometer). Canada was considered taking into account the islands, this is undoubtedly; how the oceans were thought to be unknown, but the coastlines of two of the three oceans that surround Canada are, in total, less than the coastline of Canada alone. For Norway, a figure of 21,925 km is given and a note is given: “Mainland 3419 km, large islands 2413 km, long fjords, numerous small islands and shallow bends [literally notches] coastline 16 093 km ". The sum is just the indicated total length of the coastline. But that's why the shores of the fjords are not part of the coastline of the mainland, why the length of the notches is added to the length of the coastline of the mainland, which islands are considered large - all this can only be guessed at. Absolutely indisputable data in this table are given only for Andorra, Austria, Botswana, Hungary, Swaziland and similar countries that do not have access to the sea - it is written: "0 km".

Since land has features at all levels, from hundreds of kilometers in size to tiny fractions of a millimeter and below, there is no obvious size limit for the smallest features, and therefore no well-defined land perimeter is fixed. Different approximations exist under certain minimum size assumptions.

An example of a paradox is the well-known UK coast... If the UK coastline is measured using fractal units of 100 km (62 mi) in length, then the coastline is approximately 2,800 km (1,700 mi) long. With a unit of 50 km (31 mi), the total length is about 3,400 km (2,100 mi), about 600 km (370 mi) longer.

Mathematical aspects

The basic concept of length comes from Euclidean distance... In a friend Euclidean geometry, a straight line represents the shortest distance between two points; this line has only one finite length. The geodetic length on the surface of a sphere, called the great length of a circle, is measured along the surface of a curve that exists in a plane that contains the endpoints of a path and the center of the sphere. The length of the main curve is more complex, but can also be calculated. By measuring with a ruler, a person can approximate the lengths of the curve by adding the sum of straight lines connecting the points:

Using several straight lines close to the length of the curve will produce a low estimate. Using shorter and shorter lines will produce a sum of lengths that approaches the true length of the curve. The exact value of this length can be established using calculus, a branch of mathematics that allows you to calculate infinitely small distances. The following animation illustrates this example:

However, not all curves can be measured this way. By definition, a fractal curve is a curve with complex changes in the measurement scale. Taking into account the approximation of the smooth curve closer and closer to one value as the measurement accuracy increases, the measured value of fractals can change significantly.

Length " true fractal"always tends to infinity. However, this figure is based on the idea that space can be subdivided to uncertainty, that is, be unlimited. This is the fantasy that underlies Euclidean geometry and serves as a useful model in everyday dimensions, almost certainly does not reflect the changing realities of “space” and “distance” at the atomic level Shorelines are different from mathematical fractals, they are formed from numerous small details that create models only statistically.

For practical reasons, you can use the dimension with an appropriate choice of the minimum ordinal size. If the coastline is measured in kilometers, then small variations are much less than one kilometer and are easy to ignore. To measure the coastline in centimeters, tiny changes in size must be considered. Using different measurement techniques for different units also destroys the usual belief that blocks can be transformed by simple multiplication. Coastline extremes include the fjords paradox of the heavy coasts of Norway, Chile, and the Pacific coast of North America.

Shortly before 1951, Lewis Fry Richardson, in a study of the possible influence of the length of the border on the likelihood of war, noticed that the Portuguese presented their measured border with Spain, a length of 987 km, but Spain reported it as 1214 km. This was the beginning of the coastline problem, which is mathematically difficult to measure due to the irregularity of the line itself. The predominant method for estimating the length of a border (or coastline) was to overlay N numbers of equal ℓ delimited segments on a map or aerial photograph. Each end of the segment should be on the border. By examining the discrepancies in boundary estimates, Richardson discovered what is now called the Richardson effect: the sum of the segments is inversely proportional to the total length of the segments. In fact, the shorter the ruler, the larger the measured border; by Spanish and Portuguese geographers, the border was simply measured using different ruler lengths. As a result, Richardson was struck by the fact that, under certain circumstances, when the length of the ruler ℓ tends to zero, the length of the coastline also tends to infinity. Richardson believes that on the basis of Euclidean geometry, the coastline will approach a fixed length, how to make similar estimates of regular geometric shapes. For example, the perimeter of a regular polygon inscribed in a circle approaches a circle with an increase in the number of sides (and a decrease in the length of one side). In geometric measure theory, such a smooth curve as a circle, to which small straight segments with a certain limit can be approached, is called a rectifiable curve.

More than ten years after Richardson completed his job, Benoit Mandelbrot developed a new area of ​​mathematics - fractal geometry to describe just such non-rectifiable complexes in nature in the form of an endless coastline. Own definition of a new figure, serving as the basis for his research: I came up with a fractal from the Latin adjective “ fragmented»To create irregular fragments. It is therefore advisable ... that, in addition to "fragmented" ... broken should also mean "irregular".

The key property of a fractal is self-similarity, that is, the same general configuration appears at any scale. The coastline is perceived as interspersed with headlands. In a hypothetical situation, a given coast has this property of self-similarity, no matter how much any small stretch of coast is magnified, a similar pattern of smaller bays and headlands overlaps large bays and headlands, down to a grain of sand. In this case, the scale of the coastline instantly changes into a potentially infinitely long thread with a random arrangement of bays and capes formed from small objects. Under these conditions (as opposed to smooth curves), Mandelbrot argues, “The length of the coastline turns out to be an elusive concept that slides between the fingers of those who want to understand it.” There are different kinds of fractals. The coastline with the specified parameters is in the "first category of fractals, namely, curves with fractal dimension greater than 1. "This last statement is an extension of Richardson's thought by Mandelbrot.

Mandelbrot's Richardson Effect statement:

where L, the length of the coastline, a function of the unit, ε, is approximated by. F is constant and D is Richardson's parameter. He did not provide a theoretical explanation, but Mandelbrot defined D with a non-integer form Hausdorff dimension, later - fractal dimension. Rearranging the right side of the expression, we get:

where Fε-D must be the number of ε units required to obtain L. Fractal dimension- the number of fractal sizes used to approximate the fractal: 0 for a point, 1 for a line, 2 for an area. The D in the expression is between 1 and 2, for the coast it is usually less than 1.5. The coastal polyline dimension does not extend in one direction and does not represent an area, but is intermediate. This can be interpreted as thick lines or stripes 2ε wide. More broken coastlines have greater D and, therefore, L greater, for the same ε. Mandelbrot showed that D does not depend on ε.

Source: http://en.wikipedia.org/wiki/Coast#Coastline_problem

http://en.wikipedia.org/wiki/Coastline_paradox

Translation: Dmitry Shakhov

Country Canada is one of the countries with the largest territory in the world, ranking second after Russia. The territory of Canada is 9 984 670 km², while the population of the country in 2016 was 36 048 521 people. But the density of the country is only 3.5 people per km2, which is one of the lowest in the world. Canada is also famous for the longest coastline in the world - 243 791 km! Canada is located on the mainland of North America, in its northern part. It has a land border only with the United States, and has sea borders with Denmark (Greenland) and France (Saint-Pierre and Miquelon).

Canada is washed in the north by the Arctic Ocean, in the west by the Pacific Ocean, and in the east by Canada by the Atlantic Ocean. The length of Canada from north to south of the country is 4600 km, and from west to east of the country - 7700 km.

The capital of Canada is Ottawa. The monetary unit is the Canadian dollar. The monarch of Canada today is Elizabeth II.

Canada is a constitutional monarchy with a parliamentary system. It was founded in 1534 by J. Cartier. The country consists of 3 territories and 10 provinces. The country has two official languages ​​- English and French.

Flag of Canada:

Today this country is an industrially and technologically advanced state. Canada has a diversified economy that relies on trade and natural resources, which Canada is rich in.

Relief of canada

The central part of the country is occupied by plains. It is possible to distinguish the Hudson Bay Lowland, which is marked by a flat relief, the Laurentian Upland, which is characterized by hilly relief and the central plains. In the west of the country is the Cordillera mountain system. The highest point is Mount Logan of this mountain system, which reaches 5959 meters above sea level. In the northeast of the country there is a strip of mountains up to 2000 m high, and in the southeast there is an area of ​​the Appalachian Uplands.

Climate of Canada

The climate of Canada is quite diverse, due to its large territory. In total, Canada has three types of climatic zones - Arctic, Subarctic and temperate. Temperatures are very different in the north and south of the country. In winter, the difference in average temperatures in the south and north reaches almost 30 units, and in summer it is slightly less.

For example, the average maximum temperature in the north in winter reaches -28 degrees Celsius, and in the south of the country -0.4 degrees Celsius. In summer, the average maximum temperature in the north reaches 6 degrees Celsius, and in the south of the country 29 degrees Celsius. At the same time, in the summer in the south of the country, the temperature can rise to 35-40 degrees Celsius, and in the north of the country, drop to -45-60 degrees Celsius with strong icy winds.

The climate in Canada is rather harsh. These are long, snowy winters that last up to 8 months a year and short summers. At the same time, in winter in the south of the country the sun shines 8 hours a day, and in the north it does not shine at all. Since icy winds from the north and warm winds blowing from the United States meet on the territory of the country, a rather large amount of precipitation falls over Canada.

Inland waters of Canada

Canada is one of the first in terms of the number of lakes. About 10% of Canada's area is covered with water. On its territory are the Great Lakes (Ontario, Superior, Erie, Huron), as well as smaller lakes and numerous rivers throughout the country. The most important river in Canada is the navigable St. Lawrence River, which connects the Great Lakes to the Atlantic Basin. Thanks to the climate of Canada, all its lakes and rivers are covered with ice from 5 to 9 months a year.

The flora of Canada

The vegetation in the country varies from deciduous and mixed forests in the south of the country to tundra, taiga, which in the north of the country turn into arctic deserts. Coniferous forests prevail among the forests in Canada. In the forests, most often you can find such plants as: black spruce, pine, white spruce, thuja, larch, oak, beech, chestnut, alder, birch, willow, cedar, fir, strawberry tree, elm and many other plants.

Fauna of Canada

In the south of the country, the fauna is the most diverse, and in the north it is the most scarce. On the territory of the country there are deer, moose, rams, goats, arctic fox, hare, chikari squirrel, chipmunks, jerboas, porcupines, American flying squirrel, beaver, raccoon, wolf, fox, bears and many other representatives of animals. There are also many migratory and game birds. Rivers and lakes are rich in fish. But the list of reptiles and amphibians is not so numerous.

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