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Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere.
The concept of angles between lines (in the plane or in space), between two planes (dihedral angle) or between a line and a plane can be generalized to arbitrary dimensions. This generalization was first discussed by Camille Jordan . [ 1 ]
An angle equal to 1 / 4 turn (90° or π / 2 radians) is called a right angle. Two lines that form a right angle are said to be normal, orthogonal, or perpendicular. [12] An angle larger than a right angle and smaller than a straight angle (between 90° and 180°) is called an obtuse angle [11] ("obtuse" meaning "blunt").
In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are the radial distance r along the line connecting the point to a fixed point called the origin; the polar angle θ between this radial line and a given polar axis; [a] and
The angle of two lines is defined as follows. If θ is the angle of two segments, one on each line, the angle of any two other segments, one on each line, is either θ or π − θ. One of these angles is in the interval [0, π/2], and the other being in [π/2, π]. The non-oriented angle of the two lines is the one in the interval [0, π/2].
In a Euclidean space: There is the distance between a flat and a point. (See for example Distance from a point to a plane and Distance from a point to a line.) There is the distance between two flats, equal to 0 if they intersect. (See for example Distance between two parallel lines (in the same plane) and Skew lines § Distance.)
If developed as a part of solid geometry, use is made of points, straight lines and planes (in the Euclidean sense) in the surrounding space. In spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles ...
For example, the orientation in space of a line, line segment, or vector can be specified with only two values, for example two direction cosines. Another example is the position of a point on the Earth, often described using the orientation of a line joining it with the Earth's center, measured using the two angles of longitude and latitude.