What is a coordinate system?

Every modern person is obliged to know thatis a coordinate system. Every day we come across such systems without even thinking what they are. Once in school we learned the basic concepts, we somehow know that there is an X-axis, an axis of igrovki and a zero point. In fact, everything is much more complicated, there are several types of coordinate systems. In the article we will examine each of them in detail, and also give a detailed description of where and why they are used.

Definition and scope

A coordinate system is a set of definitions,which specifies the position of the body or point using numbers or other symbols. The set of numbers that determine the location of a particular point is called the coordinates of this point. Coordinate systems are used in many areas of science, for example, in mathematics, coordinates are a collection of numbers that are mapped to points in some map of a predetermined atlas. In geometry, coordinates are values ​​that determine the location of a point in space and on a plane. In geography coordinates indicate latitude, longitude and altitude above the total sea level, ocean or other pre-known value. In astronomy, coordinates are magnitudes that make it possible to determine the position of the star, for example, declination and right ascension. This is not a complete list of where coordinate systems are used. If you think that these concepts are far from people who are not interested in science, then believe that in everyday life they are encountered much more often than you think. Take at least a map of the city, what is not the coordinate system for you?

Having dealt with the definition, let's consider what kinds of coordinate systems exist and what they are.

Zonal coordinate system

This coordinate system is used mainly forvarious horizontal surveys and the drawing up of reliable local plans. It is based on the equiangular transverse-cylindrical Gauss projection. In this projection, the entire surface of the terrestrial geoid is divided by meridians into 6-degree zones and numbered from the 1st to the 60th to the east from the Greenwich meridian. In this case, the average meridian of a given 6-coal zone is called axial. It is customary to combine it with the inner surface of the cylinder and take it as the abscissa axis. In order to avoid negative values ​​of ordinates (y), the ordinate on the axial meridian (the starting point of reference) is taken not for zero, but for 500 km, that is, move 500 km to the west. Before the ordinate, you must specify the zone number.

The Gauss-Krueger coordinate system

This coordinate system takes as a basis the projection,which suggested the famous German scientist Gauss, and developed for use in geodesy Kruger. The essence of this projection is that the terrestrial sphere is conventionally divided by meridians into six-degree zones. The zones are numbered from the Greenwich meridian from west to east. Knowing the zone number, you can easily determine the average meridian, called axial, according to the formula Z = 60 (n) - 3, where (n) is the zone number. For each zone, a flat image is made, by projecting it onto the lateral surface of the cylinder, whose axis is perpendicular to the earth's axis. Then this cylinder is deployed step by step on the plane. The equator and the axial meridian are represented by straight lines. The axis of abscissae in each zone is the axial meridian, and the equator serves as the ordinate axis. The starting point is the point of intersection of the equator and the axial meridian. The abscissa is measured to the north of the equator only with a plus sign and to the south of the equator with only a minus sign.

Polar coordinate system in the plane

This is a two-dimensional coordinate system, each point inwhich is determined on the plane by two numbers - the polar radius and the polar angle. A polar coordinate system is useful in cases where the relationship between points is easier to represent in the form of angles and radii. The polar coordinate system is given by a ray, called the polar or zero axis. The point from which the given ray emerges is called the pole or origin. An arbitrary point on the plane is determined only by two polar coordinates: angular and radial. The radial coordinate equals the distance from the point to the origin of the coordinate system. The angular coordinate is equal to the angle at which you need to rotate the polar axis counterclockwise to get to the point.

Rectangular coordinate system

What is a rectangular coordinate system for youprobably already known from the school bench, but still, let's remember again. A rectangular coordinate system is a rectilinear system in which the axes are arranged in space or on a plane and mutually perpendicular to each other. This is the most simple and often used coordinate system. It directly and fairly easily generalizes for spaces with any dimension, which also contributes to its widest application. The position of the point on the plane is determined by two coordinates - x and y, respectively, there is an axis of abscissae and ordinates.

Cartesian coordinate system

Explaining what a Cartesian coordinate system is, inFirst of all it is necessary to say that this is a particular case of a rectangular coordinate system in which the same scales are set along the axes. In mathematics, the two-dimensional or three-dimensional Cartesian coordinate system is most often considered. The coordinates are denoted by the Latin letters x, y, z and are called the abscissa, ordinate and applicate respectively. The coordinate axis (OX) is usually called the abscissa axis, the axis (OY) - the axis of ordinates, and the axis (OZ) - the axis of the applicator.

Now you know what a coordinate system is, what they are and where they are used.

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