The Collaborative International Dictionary
Conic \Con"ic\, Conical \Con"ic*al\, a. [Gr. ?: cf. F. conique. See Cone.]
Having the form of, or resembling, a geometrical cone; round and tapering to a point, or gradually lessening in circumference; as, a conic or conical figure; a conical vessel.
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Of or pertaining to a cone; as, conic sections.
Conic section (Geom.), a curved line formed by the intersection of the surface of a right cone and a plane. The conic sections are the parabola, ellipse, and hyperbola. The right lines and the circle which result from certain positions of the plane are sometimes, though not generally included.
Conic sections, that branch of geometry which treats of the parabola, ellipse, and hyperbola.
Conical pendulum. See Pendulum.
Conical projection, a method of delineating the surface of a sphere upon a plane surface as if projected upon the surface of a cone; -- much used by makers of maps in Europe.
Conical surface (Geom.), a surface described by a right line moving along any curve and always passing through a fixed point that is not in the plane of that curve.
Wiktionary
n. (context geometry English) Any of the four distinct shapes that are the intersections of a cone with a plane, namely the circle, ellipse, parabola and hyperbola.
WordNet
n. (geometry) a curve generated by the intersection of a plane and a circular cone [syn: conic]
Wikipedia
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse. The circle is a special case of the ellipse, and is of sufficient interest in its own right that it was sometimes called a fourth type of conic section. The conic sections have been studied by the ancient Greek mathematicians with this work culminating around 200 BC, when Apollonius of Perga undertook a systematic study of their properties.
There are many distinguishing properties that the conic sections of the Euclidean plane have and many of these can, and have been, used as the basis for a definition of the conic sections. A geometric property that has been used defines a non-circular conic to be the set of those points whose distances to some particular point, called a focus, and some particular line, called a directrix, are in a fixed ratio, called the eccentricity. The type of conic is determined by the value of the eccentricity. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2, that is, as the set of points whose coordinates satisfy a quadratic equation in two variables. This equation may be written in matrix form and some geometric properties can be studied as algebraic conditions.
In the Euclidean plane, the conic sections appear to be quite different from one another yet they share many similar properties. By extending the geometry to a projective plane (adding a line at infinity) this appearance disappears and the commonality becomes apparent. Further extension, by expanding the real coordinates to admit complex coordinates provides the means to see this unification algebraically.
Usage examples of "conic section".
In algebraic geometry a circle ended up being defined as `a conic section that passes through the two imaginary circular points at infinity', which sure puts a pair of compasses in their place.
Like the shoreline of Cone, the conic section, where the land folk meet the sea folk for love.
And a stream of migrant evenings, of which a sort of conic section cut through the sky made visible the successive layers, pink, blue and green, were gathered in readiness for departure to warmer climes.