for r ≠ 0 and r ≠ 1, can be treated as defining a generalized parabola. The idea of generalized conic has found applications in approximation theory and...

Cone (linear algebra) Cylinder (geometry) Democritus Elliptic cone Generalized conic Hyperboloid List of shapes Pyrometric cone Quadric Rotation of axes...

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola...

Hildesheim: Georg Olms, 1964. List of German inventors and discoverers Generalized conic Biography of Ehrenfried Walther von Tschirnhaus Archived 2013-11-28...

theory Coherent system of units Chaos theory Dimensional analysis Generalized conic Singularity Structural rigidity Spouse Katherine Dewar ​ (m. 1858)​...

special case of the generalized cone. The term might refer to the solid figure bounded by the base or only to the lateral conic surface, a quadric called...

In Euclidean geometry, a triangle conic is a conic in the plane of the reference triangle and associated with it in some way. For example, the circumcircle...

sets. The conic sections can also be realized as equidistant sets. This property of conics has been used to generalize the notion of conic sections. The...

hypersphere, ellipsoid, paraboloid, or hyperboloid, is a generalization of a conic section to higher dimensions. A Taylor series is a generalization of a MacLaurin...

the sky over the course of a year Infinity symbol Lemniscates as generalized conics Lorenz attractor, a three-dimensional dynamic system exhibiting a...

generalization of Bresenham's line algorithm. The algorithm can be further generalized to conic sections. This algorithm draws all eight octants simultaneously,...

straight from pole to equator), regularly spaced along parallels. Conic In normal aspect, conic (or conical) projections map meridians as straight lines, and...

conic (a degree-2 plane curve), just as two (distinct) points determine a line (a degree-1 plane curve). There are additional subtleties for conics that...

q) is a conic, in sense 3 above. An Ostrom conic is based on a generalization of harmonic sets. Artzy has given an example of a Steiner conic in a Moufang...

animation. Bézier curves can be combined to form a Bézier spline, or generalized to higher dimensions to form Bézier surfaces. The Bézier triangle is...

the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface...

{n}{n/2}}.} : (Thm. 1.1)  n-ellipses are special cases of spectrahedra. Generalized conic Geometric median J. Sekino (1999): "n-Ellipses and the Minimum Distance...

conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic...

sometimes used for the diameter of a conic section. In this context, a diameter is any chord which passes through the conic's centre. A diameter of an ellipse...

curves is constructed. For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and...

base edge and apex form a triangle, called a lateral face. A pyramid is a conic solid with a polygonal base. Many types of pyramids can be found by determining...

be generalized from circles to other conic sections which are the ellipse, hyperbola and parabola. This generalization is possible because conic sections...

In geometry, two conic sections are called confocal if they have the same foci. Because ellipses and hyperbolas have two foci, there are confocal ellipses...

object can be used in a pencil. The common ones are lines, planes, circles, conics, spheres, and general curves. Even points can be used. A pencil of points...

track of satellites in polar orbit. The analog of a conic section on the sphere is a spherical conic, a quartic curve which can be defined in several equivalent...

intersecting conics to solve cubics had been used earlier by Menaechmus, Archimedes, and Alhazan, but Omar Khayyam took the praiseworthy step of generalizing the...

a synthetic construction of the conic defined by five points, by varying the sixth point. The theorem was generalized by August Ferdinand Möbius in 1847...

non-degenerate conic section given by equation (9) can be identified by evaluating B 2 − 4 A C {\displaystyle B^{2}-4AC} . The conic section is: an ellipse...

faces of a fixed tetrahedron are given by two conics intersecting in four nodes. Tetrahedroids generalize Fresnel's wave surface. Cayley, Arthur (1846)...

incidence properties. The standard examples are the nondegenerate conics. However, a conic is only defined in a pappian plane, whereas an oval may exist in...