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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 ...
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 general, a conical surface consists of two congruent unbounded halves joined by the apex. Each half is called a nappe, and is the union of all the rays that start at the apex and pass through a point of some fixed space curve. [2] Sometimes the term "conical surface" is used to mean just one nappe. [3]
Live Geometry is a free CodePlex project that lets you create interactive ruler and compass constructions and experiment with them. It is written in Silverlight 4 and C# 4.0 (Visual Studio 2010). The core engine is a flexible and extensible framework that allows easy addition of new figure types and features.
More generally, given a vector bundle (finite-rank locally free sheaf) E on X, if R=Sym(E *) is the symmetric algebra generated by the dual of E, then the cone is the total space of E, often written just as E, and the projective cone is the projective bundle of E, which is written as ().
General solutions are a class of solutions within descriptive geometry that contain all possible solutions to a problem. The general solution is represented by a single, three-dimensional object, usually a cone, the directions of the elements of which are the desired direction of viewing (projection) for any of an infinite number of solution views.
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The ball may be thought of as the 'lid' at the base of the 4-dimensional cone's nappe, and the origin becomes its 'apex'. This shape may be projected into 3-dimensional space in various ways. If projected onto the xyz hyperplane, its image is a ball. If projected onto the xyw, xzw, or yzw hyperplanes, its image is a solid cone.