Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-17th century, though the actual term "polar coordinates" has been attributed to Gregorio Fontana in the 18th century. Angles in polar notation are generally expressed in either degrees or radians (2 π rad being equal to 360°). The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. 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 reference point and an angle from a reference direction.
![graph spherical coordinates graph spherical coordinates](https://image1.slideserve.com/2998265/figure-11-75-l.jpg)
In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3, 60°). Coordinates comprising a distance and an angle Points in the polar coordinate system with pole O and polar axis L. The command to create the plot from the Plotting Guide is 2 Pi, coords = z_cylindrical, title = z_cylindrical, orientation = − 132, 71, axes = boxed Pi, coords = toroidal 2, style = wireframeĭefine a new cylindrical system so z = z r, θ instead of r = r θ, z :Īddcoords z_cylindrical, z, r, &theta, r cos &theta, r sin &theta, z Pi, coords = spherical, style = wireframe Pi, coords = spherical, scaling = constrained Īll coordinate systems are also valid for parametrically defined 3-D plots with the same interpretations of the coordinate system transformations. The conversions from the various coordinate systems to Cartesian coordinates can be found in coords. Other coordinate systems have similar interpretations. A second convention for spherical coordinates is also available, called spherical_physics, in which the meanings of the second and third coordinates are swapped. These angles determine the direction from the origin while the distance from the origin, r, is a function of phi and theta. phi is the angle measured from the positive z-axis, or the colatitude.
![graph spherical coordinates graph spherical coordinates](https://i.pinimg.com/originals/c1/47/74/c14774d059de199a03c6c12da4b50ba5.png)
Where theta is the counterclockwise angle measured from the x-axis in the x-y plane.
![graph spherical coordinates graph spherical coordinates](https://i.ytimg.com/vi/yR3lFfupSdo/maxresdefault.jpg)
R, the distance to the projection of the point in the x-y plane from the origin, is a function of theta, the counterclockwise angle from the positive x-axis, and of z, the height above the x-y plane.įor spherical coordinates the interpretation is: plot3d r θ, φ, θ = a. For example, when using cylindrical coordinates, Maple expects the command to be of the following form: plot3d r θ, z, θ = a. įor alternate coordinate systems this is interpreted differently. When using Cartesian coordinates, z, the vertical coordinate, is expressed as a function of x and y: plot3d z x, y, x = a. įor a description of each of the above coordinate systems, see the coords help page. The alternate choices are: bipolarcylindrical, bispherical, cardioidal, cardioidcylindrical, casscylindrical, confocalellip, confocalparab, conical, cylindrical, ellcylindrical, ellipsoidal, hypercylindrical, invcasscylindrical, invellcylindrical, invoblspheroidal, invprospheroidal, logcoshcylindrical, logcylindrical, maxwellcylindrical, oblatespheroidal, paraboloidal, paracylindrical, prolatespheroidal, rosecylindrical, sixsphere, spherical, spherical_math, spherical_physics, tangentcylindrical, tangentsphere, and toroidal. The coords option allows the user to alter this coordinate system. The default coordinate system for all three dimensional plotting commands is the Cartesian coordinate system.