Mathematical expression of circle like slices of sphere
"Small circle" redirects here. For the typographical symbol, see Degree symbol.
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Small circle of a sphere.
In spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical radius) from a given point on the sphere (the pole or spherical center). It is a curve of constant geodesic curvature relative to the sphere, analogous to a line or circle in the Euclidean plane; the curves analogous to straight lines are called great circles, and the curves analogous to planar circles are called small circles or lesser circles. If the sphere is embedded in three-dimensional Euclidean space, its circles are the intersections of the sphere with planes, and the great circles are intersections with planes passing through the center of the sphere.
spherical geometry, a sphericalcircle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical radius)...
great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. The origins of spherical trigonometry...
points and (straight) lines. In spherical geometry, the basic concepts are point and great circle. However, two great circles on a plane intersect in two...
including the parallel postulate. In spherical trigonometry, angles are defined between great circles. Spherical trigonometry differs from ordinary trigonometry...
enclosed by a circle of radius R in a flat space is always greater than the area of a sphericalcircle and smaller than a hyperbolic circle, provided all...
arc of a great circle is a geodesic of the sphere, so that great circles in spherical geometry are the natural analog of straight lines in Euclidean space...
spherical cap and the cone formed by the center of the sphere and the base of the cap. It is the three-dimensional analogue of the sector of a circle...
The roughly spherical shape of Earth can be empirically evidenced by many different types of observation, ranging from ground level, flight, or orbit...
great circle), so that the height of the cap is equal to the radius of the sphere, the spherical cap is called a hemisphere. The volume of the spherical cap...
sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular...
In spherical geometry, a spherical lune (or biangle) is an area on a sphere bounded by two half great circles which meet at antipodal points. It is an...
multiplied by the anamorphic power of the camera lenses (1× in the case of spherical lenses). Gate dimensions are the width and height of the camera gate aperture...
sphericity less than 1. Sphericity applies in three dimensions; its analogue in two dimensions, such as the cross sectional circles along a cylindrical object...
of the circle and the centre is called the radius. The circle has been known since before the beginning of recorded history. Natural circles are common...
the Euclidean, spherical, and hyperbolic cases of the law of sines described above. Let pK(r) indicate the circumference of a circle of radius r in a...
as in the planar case, a spherical conic can be defined as the locus of points the sum or difference of whose great-circle distances to two foci is constant...
where: d is the distance between the two points along a great circle of the sphere (see spherical distance), r is the radius of the sphere. The haversine formula...
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...
path is, in fact, the spherical geometry equivalent of a path along a line segment in the plane; a great circle is a spherical geodesic. More familiar...
"carrying around") is the perimeter of a circle or ellipse. The circumference is the arc length of the circle, as if it were opened up and straightened...
the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square with the area of a given circle by...
coordinates. Spherical Bessel functions with half-integer α {\displaystyle \alpha } are obtained when solving the Helmholtz equation in spherical coordinates...
Gall-Peters projection, a circle of latitude is perpendicular to all meridians. On the ellipsoid or on spherical projection, all circles of latitude are rhumb...
has undergone a recent resurgence as a conspiracy theory. The idea of a spherical Earth appeared in ancient Greek philosophy with Pythagoras (6th century...
latitude, as defined in this way for the sphere, is often termed the spherical latitude, to avoid ambiguity with the geodetic latitude and the auxiliary...
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