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The solution of the Kepler problem in a space of uniform positive curvature is a spherical conic, with a potential proportional to the cotangent of geodesic distance. [ 5 ] Because it preserves distances to a pair of specified points, the two-point equidistant projection maps the family of confocal conics on the sphere onto two families of ...
The elliptic cones intersect the sphere in spherical conics. Conical coordinates , sometimes called sphero-conal or sphero-conical coordinates, are a three-dimensional orthogonal coordinate system consisting of concentric spheres (described by their radius r ) and by two families of perpendicular elliptic cones, aligned along the z - and x ...
All curves are circles or straight lines. The generatrices and parallels generates a 3D dual cone. The hypermeridians generates a set of concentric spheres. In geometry, a hypercone (or spherical cone) is the figure in the 4-dimensional Euclidean space represented by the equation + + =
From the fact, that the affine image of a conic section is a conic section of the same type (ellipse, parabola,...), one gets: Any plane section of an elliptic cone is a conic section. Obviously, any right circular cone contains circles. This is also true, but less obvious, in the general case (see circular section).
The analog of a conic section on the sphere is a spherical conic, a quartic curve which can be defined in several equivalent ways. The intersection of a sphere with a quadratic cone whose vertex is the sphere center; The intersection of a sphere with an elliptic or hyperbolic cylinder whose axis passes through the sphere center
In geometry, a spherical sector, [1] also known as a spherical cone, [2] is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere. It can be described as the union of a spherical cap and the cone formed by the center of the sphere and the base of the cap.
The equation for a conic section with apex at the origin and tangent to the y axis is + (+) = alternately = + (+) where R is the radius of curvature at x = 0. This formulation is used in geometric optics to specify oblate elliptical ( K > 0 ), spherical ( K = 0 ), prolate elliptical ( 0 > K > −1 ), parabolic ( K = −1 ), and hyperbolic ( K ...
Download as PDF; Printable version ... hide. A spherical cone may mean: a hypercone in 4D; a spherical sector in 3D; See also. Spherical conic This page was last ...