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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.
Conical spiral with an archimedean spiral as floor projection Floor projection: Fermat's spiral Floor projection: logarithmic spiral Floor projection: hyperbolic spiral. In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral.
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. [4] [5]
A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes).It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
In geometry, a hypercone (or spherical cone) is the figure in the 4-dimensional Euclidean space represented by the equation x 2 + y 2 + z 2 − w 2 = 0. {\displaystyle x^{2}+y^{2}+z^{2}-w^{2}=0.} It is a quadric surface, and is one of the possible 3- manifolds which are 4-dimensional equivalents of the conical surface in 3 dimensions.
The external surface area A of the cap equals r2 only if solid angle of the cone is exactly 1 steradian. Hence, in this figure θ = A/2 and r = 1. The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2 θ, is the area of a spherical cap on a unit sphere
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 cone over two points {0, 1} is a "V" shape with endpoints at {0} and {1}. The cone over a closed interval I of the real line is a filled-in triangle (with one of the edges being I), otherwise known as a 2-simplex (see the final example). The cone over a polygon P is a pyramid with base P.