A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs of great circles on a sphere. It is measured by the angle between the planes containing the arcs (which naturally also contain the centre of the sphere).[1]
^Green, Robin Michael (1985). Spherical Astronomy. Cambridge University Press. p. 3. ISBN 9780521317795.
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified...
A sphericalangle is a particular dihedral angle; it is the angle between two intersecting arcs of great circles on a sphere. It is measured by the angle...
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles...
a cone with its apex at the apex of the solid angle, and with apex angle 2θ, is the area of a spherical cap on a unit sphere Ω = 2 π ( 1 − cos θ ) ...
sense) in the surrounding space. In spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary...
of spherical harmonics. Subsequently, in his 1782 memoir, Laplace investigated these coefficients using spherical coordinates to represent the angle γ...
where Ω is the solid angle of the spherical sector in steradians, the SI unit of solid angle. One steradian is defined as the solid angle subtended by a cap...
The roughly spherical shape of Earth can be empirically evidenced by many different types of observation, ranging from ground level, flight, or orbit...
become much simpler if one of the angles of a triangle (for example, the angle C) is the right angle. Such a spherical triangle is fully defined by its...
\end{aligned}}} This angle corresponds to the plane aperture angle of 2θ ≈ 1.144 rad or 65.54°. A steradian is also equal to the spherical area of a polygon...
to zero. For a spherical triangle, the sum of the angles is greater than 180° and can be up to 540°. Specifically, the sum of the angles is 180° × (1 +...
This page uses common physics notation for spherical coordinates, in which θ {\displaystyle \theta } is the angle between the z axis and the radius vector...
geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's base). The angle between...
those respective sides. These are dihedral angles between the planes of the three great circles. Then the spherical law of sines says: sin A sin a = sin...
The central angle is also known as the arc's angular distance. The arc length spanned by a central angle on a sphere is called spherical distance. The...
In an automobile, ball joints are spherical bearings that connect the control arms to the steering knuckles, and are used on virtually every automobile...
In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles...
which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): The polar angle is denoted by θ ∈ [ 0 , π ]...
sharing the vertex. The angle may be quantified using a single number by the interior solid angle at the vertex (the spherical excess), which is related...
than a spherical mirror can. A toroidal reflector is a form of parabolic reflector which has a different focal distance depending on the angle of the...
two right spherical triangles. The surface area of a spherical lune is 2θ R2, where R is the radius of the sphere and θ is the dihedral angle in radians...
directions') is the angular measurement in a spherical coordinate system which represents the horizontal angle from a cardinal direction, most commonly north...
functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side...
continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the...
In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or π {\displaystyle \pi } /2 radians corresponding to a quarter turn. If...
proved. The exterior angle theorem is not valid in spherical geometry nor in the related elliptical geometry. Consider a spherical triangle one of whose...
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