An elliptical cone is a cone with an elliptical base. published in Acta Eruditorum, 1734 A cone truncated by an inclined planeĪ cone with a region including its apex cut off by a plane is called a truncated cone if the truncation plane is parallel to the cone's base, it is called a frustum. Illustration from Problemata mathematica. In optics, the angle θ is called the half-angle of the cone, to distinguish it from the aperture. The aperture of a right circular cone is the maximum angle between two generatrix lines if the generatrix makes an angle θ to the axis, the aperture is 2 θ. The "base radius" of a circular cone is the radius of its base often this is simply called the radius of the cone. (For the connection between this sense of the term "directrix" and the directrix of a conic section, see Dandelin spheres.) The perimeter of the base of a cone is called the "directrix", and each of the line segments between the directrix and apex is a "generatrix" or "generating line" of the lateral surface. Air traffic control tower in the shape of a cone, Sharjah Airport.Ī cone with a polygonal base is called a pyramid.ĭepending on the context, "cone" may also mean specifically a convex cone or a projective cone.Ĭones can also be generalized to higher dimensions. Contrasted with right cones are oblique cones, in which the axis passes through the centre of the base non-perpendicularly. 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). If the cone is right circular the intersection of a plane with the lateral surface is a conic section. 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. 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. Either half of a double cone on one side of the apex is called a nappe. 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. 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 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. 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. 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. ![]() A right circular cone with the radius of its base r, its height h, its slant height c and its angle θ.Ī right circular cone and an oblique circular cone A double cone (not shown infinitely extended) 3D model of a coneĪ 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.Ī 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.
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