Conical
cone is a basic shape in geometry. Several things have also been called cones on account of their shape:
The word cone and its derivatives also have several specialized meanings in mathematics:
- In geometry, cone is often used informally for conical surface, usually a right circular one; see cone (geometry).
- Also in geometry, the cone of an arbitrary set <math>X<math> means the union of all line segments connecting a fixed point to points of <math>X<math>. For exmple, this coning operation will turn a triangle into a tetrahedron.
- In topology, too, coning may be applied to a topological space, e.g. to define the barycentric subdivision of a cell complex; see cone (topology).
- In linear algebra, the convex cone of a set of vectors consists of all linear combinations of those vectors with non-negative coefficients.
- In descriptive geometry, "conical projection" is another name for the perspective projection.
- In cartography, however, a conical projection maps the spherical surface of the Earth to a conical surface, that is then unrolled onto a plane.
- A conic section is any curve obtained by cutting the surface of a cone (more precisely, a conical surface) by an arbitrary plane.
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