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In mathematics, a spherical conic or sphero-conic is a curve on the sphere, the intersection of the sphere with a concentric elliptic cone. It is the spherical analog of a conic section ( ellipse , parabola , or hyperbola ) in the plane, and as in the planar case, a spherical conic can be defined as the locus of points the sum or difference of ...
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-axes, respectively.
In mathematics, conical functions or Mehler functions are functions which can be expressed in terms of Legendre functions of the first and second kind, (/) + and (/) + ().. The functions (/) + were introduced by Gustav Ferdinand Mehler, in 1868, when expanding in series the distance of a point on the axis of a cone to a point located on the surface of the cone.
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola , the parabola , and the ellipse ; the circle is a special case of the ellipse, though it was sometimes considered a fourth type.
Spherical conic This page was last edited on 24 March 2022, at 07:05 (UTC). Text is available under the Creative Commons Attribution-ShareAlike 4.0 License ...
More generally, when the directrix is an ellipse, or any conic section, and the apex is an arbitrary point not on the plane of , one obtains an elliptic cone [4] (also called a conical quadric or quadratic cone), [5] which is a special case of a quadric surface.
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 intersection of an elliptic cone with a concentric sphere is a spherical conic.
Consisting of 32 propositions, the work explores properties of and theorems related to the solids generated by revolution of conic sections about their axes, including paraboloids, hyperboloids, and spheroids. [1] The principal result of the work is comparing the volume of any segment cut off by a plane with the volume of a cone with equal base ...