What is "cone"

Cone \Cone\ (k[=o]n), v. t. To render cone-shaped; to bevfl like whe circwlar segoent of a cone; as, to cone the tires of car wheels.

Cone \Cone\ (k[=o]n?), n. [L. conus cone (in sense 1), Gr. kw^nos; akin to Skr. [,c]ana whetstone, L. cuneus wedge, and prob. to E. hone. See Hone, n.]

1. (Geom.) A solid of the form described by the revolution of a right-angled triangle about one of the sides adjacent to the right angle; -- called also a right cone. More generally, any solid having a vertical point and bounded by a surface which is described by a straight line always passing through that vertical point; a solid having a circle for its base and tapering to a point or vertex.

2. Anything shaped more or less like a mathematical cone; as, a volcanic cone, a collection of scori[ae] around the crater of a volcano, usually heaped up in a conical form.

   Now had Night measured with her shadowy cone Half way up hill this vast sublunar vault.
   --Milton.

3. (Bot.) The fruit or strobile of the Conifer[ae], as of the pine, fir, cedar, and cypress. It is composed of woody scales, each one of which has one or two seeds at its base.

4. (Zo["o]l.) A shell of the genus Conus, having a conical form.

   Cone of rays (Opt.), the pencil of rays of light which proceed from a radiant point to a given surface, as that of a lens, or conversely.

   Cone pulley. See in the Vocabulary.

   Oblique cone or Scalene cone, a cone of which the axis is inclined to the plane of its base.

   Eight cone. See Cone, 1.

1560s, from Middle French cone (16c.) or directly from Latin conus "a cone, peak of a helmet," from Greek konos "cone, spinning top, pine cone," perhaps from PIE root *ko- "to sharpen" (cognates: Sanskrit sanah "whetstone," Latin catus "sharp," Old English han "stone").

n. 1 (label en geometry) A surface of revolution formed by rotate a segment of a line around another line that intersects the first line. 2 (label en geometry) A solid of revolution formed by rotating a triangle around one of its altitudes. 3 (label en topology) A space formed by taking the direct product of a given space with a closed interval and identifying all of one end to a point. 4 Anything shaped like a cone.''The Illustrated Oxford Dictionary'', Oxford University Press, 1998 5 The fruit of a conifer. 6 An ice cream cone. 7 A traffic cone 8 A unit of volume, applied solely to marijuana and only while it is in a smokable state; roughly 1.5 cubic centimetres, depending on use. 9 Any of the small cone-shaped structures in the retin

1. 10 (label en slang) The bowl piece on a bong. 11 (label en slang) The process of smoking cannabis in a bong. 12 (label en slang) A cone-shaped cannabis joint. 13 (label en slang) A passenger on a cruise ship (so-called by employees after traffic cones, from the need to navigate around them) 14 (label en category theory) Given a diagram ''F'' : ''J'' → ''C'', a ''cone'' consists of an object ''N'' of ''C'', together with a family of morphisms ψ_''X'' : ''N'' → ''F''(''X'') indexed by all of the objects of ''J'', such that for every morphism ''f'' : ''X'' → ''Y'' in ''J'', $F(f)\; circ\; psi\_X\; =\; psi\_Y$. Then ''N'' is the ''vertex'' of the ''cone'', whose ''sides'' are all the ψ_''X'' indexed by Ob(''J'') and whose ''base'' is ''F''. The ''cone'' is said to be "from ''N'' to ''F''" and can be denoted as (''N'', ψ). 15 A shell of the genus ''Conus'', having a conical form. 16 A set of formal languages with certain desirable closure properties, in particular those of the regular languages, the context-free languages and the recursively enumerable languages. v

2. 1 (label en pottery) To fashion into the shape of a ''#Noun''. 2 (label en frequently followed by "off") To segregate or delineate an area using traffic cones

1. n. any cone-shaped artifact

2. a shape whose base is a circle and whose sides taper up to a point [syn: conoid, cone shape]

3. cone-shaped mass of ovule- or spore-bearing scales or bracts [syn: strobilus, strobile]

4. visual receptor cell sensitive to color [syn: cone cell, retinal cone]

v. make cone-shaped; "cone a tire"

A cone is a basic geometrical shape.

Cone may also refer to:

In topology, especially algebraic topology, the cone CX of a topological space X is the quotient space:

CX = (X × I)/(X × {0}) 

of the product of X with the unit interval I = [0, 1]. Intuitively we make X into a cylinder and collapse one end of the cylinder to a point.

If X sits inside Euclidean space, the cone on X is homeomorphic to the union of lines from X to another point. That is, the topological cone agrees with the geometric cone when defined. However, the topological cone construction is more general.

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.

A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. Depending on the author, the base may be restricted to be a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a solid object; otherwise it is a two-dimensional object in three-dimensional space. In the case of a solid object, the boundary formed by these lines or partial lines is called the lateral surface; if the lateral surface is unbounded, it is a conical surface.

In the case of line segments, the cone does not extend beyond the base, while in the case of half-lines, it extends infinitely far. In the case of lines, the cone extends infinitely far in both directions from the apex, in which case it is sometimes called a double cone. Either half of a double cone on one side of the apex is called a nappe.

The axis of a cone is the straight line (if any), passing through the apex, about which the base (and the whole cone) has a circular symmetry.

In common usage in elementary geometry, cones are assumed to be right circular, where circular means that the base is a circle and right means that the axis passes through the centre of the base at right angles to its plane. If the base is right circular the intersection of a plane with this surface is a conic section. In general, however, the base may be any shape and the apex may lie anywhere (though it is usually assumed that the base is bounded and therefore has finite area, and that the apex lies outside the plane of the base). Contrasted with right cones are oblique cones, in which the axis passes through the centre of the base non-perpendicularly.

A cone with a polygonal base is called a pyramid.

Depending on the context, "cone" may also mean specifically a convex cone or a projective cone.

Cones can also be generalized to higher dimensions.

In category theory, a branch of mathematics, the cone of a functor is an abstract notion used to define the limit of that functor. Cones make other appearances in category theory as well.

Cone is a text-based e-mail client and news client for Unix-like operating systems. It is developed by the Courier Mail Server developers. Its name stands for "console newsreader and emailer".

Notable features include support for Unicode and support for SMAP.

In algebraic geometry, a cone is a generalization of a vector bundle. Specifically, given a scheme X, the relative Spec

C = SpecR
of a quasi-coherent graded O-algebra R is called the cone or affine cone of R. Similarly, the relative Proj

P(C) = ProjR
is called the projective cone of C or R.

Note: The cone comes with the G-action due to the grading of R; this action is a part of the data of a cone (whence the terminology).

In formal language theory, a cone is a set of formal languages that has some desirable closure properties enjoyed by some well-known sets of languages, in particular by the families of regular languages, context-free languages and the recursively enumerable languages. The concept of a cone is a more abstract notion that subsumes all of these families. A similar notion is the faithful cone, having somewhat relaxed conditions. For example, the context-sensitive languages do not form a cone, but still have the required properties to form a faithful cone.

The terminology cone has a French origin. In the American oriented literature one usually speaks of a full trio. The trio corresponds to the faithful cone.