For last 40 years, thanks to modern technologies, there were more perfect methods of mapping, but still there is no way of the exact image of a curvilinear surface of the Earth on a flat sheet of paper.
the Authentic picture of the Earth can give only the globe  spherical model of our planet. However possibilities of globes are limited: even greatest of them do not give detailed representation about the Earth and a variety of its relief, they are bulky, and they are inconvenient for carrying with themselves. For practical purposes use cards of an average format. Curvature of a surface of the Earth has no value for cards of small territories, for example, for plans of cities. Cartographers have problems when it is necessary to show all globe or its considerable part on a sheet of paper. For the image of a relief of the Earth they use cartographical projections.
Cartographical projections
Appointment of such projections  precisely to display four main characteristics, namely: the area, outlines, a direction (angular interposition of points) and distance. But the card can is exact show only some of these characteristics, inevitably endowing others.
So, Flemish cartographer Gerard Merkator (151294) has become famous thanks to a cartographical projection of the Earth invented by it in 1569 Seafarers have highly appreciated the invention as the straight line connecting any two points on its card, showed exact direktsionnyj a corner between them.
Proektsija Merkatora also gave correct outlines of a land and the seas, but other characteristics, including the areas, were deformed more and more in process of removal from equator. For example, the territory of Greenland, the world's largest island, makes about 2 175 000 sq. km, and on a card of Merkatora it looks more South America occupying the space about 17 835 000 sq. km. Cartographical projections are easier for understanding if to present globe in the form of the image put on a grid of crossed horizontal and vertical lines. Horizontal are called shirotnymi as lines or parallels.
Width and a longitude
These lines are parallel to the line of equator which are passing precisely in the middle between Northern and southern poles. Parallels are measured in degrees, thus it is considered that the equator is at width +" the North Pole corresponds 90" with. sh., and the South Pole  90" ju. sh. The geographical width is a corner between a line of a plumb from the center of the Earth to the given point and an equator plane.
Longitudinal lines, or meridians, are perpendicular to parallels. All of them pass through both poles and reckon from a zero meridian. In the international practice it is considered to be that it passes through the London area Greenwich. The longitude also is measured in degrees  180" on the east and as much on the West from a zero meridian.
Creation of projections
Present the Earth in the form of the glass sphere which network of parallels at vertically directed ray of light will reject a shade on a flat surface. Present that the sphere concerns a sheet of paper in one point. The shades, rejected (projected) on a sheet of paper, form a grid named an azimuthal projection. Such kind of a projection is used for drawing up of cards of polar regions, and a contact point usually is Northern or the South Pole. For the card of Merkator used a cylindrical projection. For the description of a cylindrical projection present that the paper cylinder will wrap up round the globe, adjoining to it in the area of equator. Hence, the length of equator on a card and the globe is identical. But distortion shirotnyh and longitudinal lines increases in process of removal from equator.
The Third kind of a projection can be received if to present a paper cone, nakryvajushchii the glass sphere, concerning it on one of parallels. Such projections are called as conic.
In practice cartographers use not these three simple projections, and them matematicheski the modified variants, allowing to reduce distortions, or the projections completely received by mathematical calculations. The choice of a kind of a projection depends that it is supposed to show on a card.
