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...

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...

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

theory Coherent system of units Chaos theory Dimensional analysis Generalized conic Singularity Structural rigidity Spouse Katherine Clerk Maxwell ​ ​...

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...

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

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...

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

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...

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,...

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

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...

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...

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...

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

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

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

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...

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

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...

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

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...

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...

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...

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...

Apostol and Mamikon, has been praised for its originality and clarity. Generalized conic Visual calculus "Mamikon's Proof of the Pythagorean Theorem". Wolfram...

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...

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...