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<\/figure><\/div>\n\n\n\nPolar co-ordinate system<\/p>\n\n\n\n
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction.<\/p>\n\n\n\n
The fixed point (analogous to the origin of a Cartesian system) is called the pole, and the ray from the pole in the fixed direction is the polar axis. The distance from the pole is called the radial coordinate or radius, and the angle is the angular coordinate, polar angle, or azimuth.<\/p>\n\n\n\n
![\"image092\"](\"http:\/\/www.vskills.in\/lms\/wp-content\/uploads\/2016\/06\/image092.gif\")
<\/figure><\/div>\n\n\n\nCylindrical co-ordinate system<\/p>\n\n\n\n
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis. The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point.<\/p>\n\n\n\n
The origin of the system is the point where all three coordinates can be given as zero. This is the intersection between the reference plane and the axis. The axis is variously called the cylindrical or longitudinal axis, to differentiate it from the polar axis, which is the ray that lies in the reference plane, starting at the origin and pointing in the reference direction.<\/p>\n\n\n\n
The distance from the axis may be called the radial distance or radius, while the angular coordinate is sometimes referred to as the angular position or as the azimuth. The radius and the azimuth are together called the polar coordinates, as they correspond to a two-dimensional polar coordinate system in the plane through the point, parallel to the reference plane. The third coordinate may be called the height or altitude (if the reference plane is considered horizontal), longitudinal position, or axial position.<\/p>\n\n\n\n
Cylindrical coordinates are useful in connection with objects and phenomena that have some rotational symmetry about the longitudinal axis, such as water flow in a straight pipe with round cross-section, heat distribution in a metal cylinder, electromagnetic fields produced by an electric current in a long, straight wire, and so on.<\/p>\n\n\n\n
It is sometimes called “cylindrical polar coordinate” and “polar cylindrical coordinate”, and is sometimes used to specify the position of stars in a galaxy (“galactocentric cylindrical polar coordinate”).<\/p>\n\n\n\n
![\"image094\"](\"http:\/\/www.vskills.in\/lms\/wp-content\/uploads\/2016\/06\/image094.gif\")
<\/figure><\/div>\n\n\n\nSpherical co-ordinate system<\/p>\n\n\n\n
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.<\/p>\n\n\n\n
The radial distance is also called the radius or radial coordinate. The polar angle may be called co-altitude, zenith angle, normal angle, or inclination angle.<\/p>\n\n\n\n
The use of symbols and the order of the coordinates differs between sources. In one system frequently encountered in physics (r, \u03b8, \u03c6) gives the radial distance, polar angle, and azimuthal angle, whereas in another system used in many mathematics books (r, \u03b8, \u03c6) gives the radial distance, azimuthal angle, and polar angle. In both systems \u03c1 is often used instead of r. Other conventions are also used, so great care needs to be taken to check which one is being used.<\/p>\n\n\n\n
A number of different spherical coordinate systems following other conventions are used outside mathematics. In a geographical coordinate system positions are measured in latitude, longitude and height or altitude. There are a number of different celestial coordinate systems based on different fundamental planes and with different terms for the various coordinates. The spherical coordinate systems used in mathematics normally use radians rather than degrees and measure the azimuthal angle counter-clockwise rather than clockwise. The inclination angle is often replaced by the elevation angle measured from the reference plane. Elevation angle of zero is at the horizon.<\/p>\n\n\n\n
The concept of spherical coordinates can be extended to higher-dimensional spaces and are then referred to as hyper spherical coordinates.<\/p>\n\n\n\n
![\"image095\"](\"http:\/\/www.vskills.in\/lms\/wp-content\/uploads\/2016\/06\/image095.png\")
<\/figure><\/div>\n","protected":false},"excerpt":{"rendered":"Three-dimensional space is a geometric 3-parameters model of the physical universe (without considering time) in which all known matter exists. These three dimensions can be labeled by a combination of three chosen from the terms length, width, height, depth, and breadth. Any three directions can be chosen, provided that they do not all lie in the same plane. In physics and mathematics, a sequence of n numbers can be understood as a location…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-108605","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"\n