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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 ...
Coordinate surfaces of the conical coordinates. The constants b and c were chosen as 1 and 2, respectively. The red sphere represents r = 2, the blue elliptic cone aligned with the vertical z-axis represents μ=cosh(1) and the yellow elliptic cone aligned with the (green) x-axis corresponds to ν 2 = 2/3.
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
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 ...
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 right circular cone and an oblique circular cone A double cone (not shown infinitely extended) 3D model of a cone. A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex that is not contained in the base.
In geometry, the conic constant (or Schwarzschild constant, [1] after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K. The constant is given by K = − e 2 , {\displaystyle K=-e^{2},} where e is the eccentricity of the conic section.
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 ...