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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. The radial distance is also called the radius or radial coordinate. The polar angle may be called co-latitude, zenith angle, normal angle, or inclination angle. The use of symbols and the order of the coordinates differs between sources. In one system frequently encountered in physics (''r'', ''θ'', ''φ'') gives the radial distance, polar angle, and azimuthal angle, whereas in another system used in many mathematics books (''r'', ''θ'', ''φ'') gives the radial distance, azimuthal angle, and polar angle. In both systems ''ρ'' 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. 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 (when reference is north and the angle is increasing positively) 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. The spherical coordinate system generalises the two-dimensional polar coordinate system. It can also be extended to higher-dimensional spaces and is then referred to as a hyperspherical coordinate system. == Definition == To define a spherical coordinate system, one must choose two orthogonal directions, the ''zenith'' and the ''azimuth reference'', and an ''origin'' point in space. These choices determine a reference plane that contains the origin and is perpendicular to the zenith. The spherical coordinates of a point ''P'' are then defined as follows: * The ''radius'' or ''radial distance'' is the Euclidean distance from the origin ''O'' to ''P''. * The ''inclination'' (or ''polar angle'') is the angle between the zenith direction and the line segment ''OP''. * The ''azimuth'' (or ''azimuthal angle'') is the signed angle measured from the azimuth reference direction to the orthogonal projection of the line segment ''OP'' on the reference plane. The sign of the azimuth is determined by choosing what is a ''positive'' sense of turning about the zenith. This choice is arbitrary, and is part of the coordinate system's definition. The ''elevation'' angle is 90 degrees (π/2 radians) minus the inclination angle. If the inclination is zero or 180 degrees (π radians), the azimuth is arbitrary. If the radius is zero, both azimuth and inclination are arbitrary. In linear algebra, the vector from the origin ''O'' to the point ''P'' is often called the ''position vector'' of ''P''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Spherical coordinate system」の詳細全文を読む スポンサード リンク
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