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...

spaces. Bicone Cone (linear algebra) Cylinder (geometry) Democritus 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...

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

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...

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

{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...

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...

In planar geometry, a diameter of a conic section is typically defined as any chord which passes through the conic's centre; such diameters are not necessarily...

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

transform) Tomography Tomographic reconstruction Discrete tomography Generalized conic Gardner, R.J., Geometric Tomography, Cambridge University Press, Cambridge...

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

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

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

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...

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...

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

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...

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

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...

Apostol and Mamikon, has been praised for its originality and clarity. Generalized conic Visual calculus "Մահացել է հայտնի աստղագետ, պրոֆեսոր Մամիկոն Մնացականյանը"...

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

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...

third order contact with C. The osculating conic to C at p, the osculating curve from the family of conic sections, has fourth order contact with C. The...

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...

circles, the Spieker circle was also able to be generalized into the Spieker conic. The Spieker conic is still found within the medial triangle and touches...

Mysticum Theorem") states that if an arbitrary hexagon is inscribed in any conic section, and pairs of opposite sides are extended until they meet, the three...

points determine a conic, as long as the points are in general linear position (no three are collinear). This definition can be generalized further: one may...

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...