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...
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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...
69 KB (9,173 words) - 01:09, 4 March 2024
Cone (redirect from Conic solid)
spaces. Bicone Cone (linear algebra) Cylinder (geometry) Democritus Generalized conic Hyperboloid List of shapes Pyrometric cone Quadric Rotation of axes...
16 KB (2,283 words) - 20:14, 3 April 2024
theory Coherent system of units Chaos theory Dimensional analysis Generalized conic Singularity Structural rigidity Spouse Katherine Clerk Maxwell ...
86 KB (8,974 words) - 16:54, 22 July 2024
Equidistant set (category Conic sections)
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...
4 KB (347 words) - 05:28, 3 June 2023
Hildesheim: Georg Olms, 1964. List of German inventors and discoverers Generalized conic Biography of Ehrenfried Walther von Tschirnhaus Archived 2013-11-28...
11 KB (1,242 words) - 20:18, 20 August 2024
Parabola (redirect from Conic section/Proofs)
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...
80 KB (13,361 words) - 18:16, 27 May 2024
N-ellipse (category Conic sections)
{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...
4 KB (452 words) - 04:44, 11 April 2023
Generalization (redirect from Generalized)
hypersphere, ellipsoid, paraboloid, or hyperboloid, is a generalization of a conic section to higher dimensions. A Taylor series is a generalization of a MacLaurin...
7 KB (826 words) - 15:43, 12 June 2024
Diameter (redirect from Generalized diameter)
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...
8 KB (1,003 words) - 19:27, 26 June 2024
straight from pole to equator), regularly spaced along parallels. Conic In normal aspect, conic (or conical) projections map meridians as straight lines, and...
31 KB (780 words) - 22:58, 17 August 2024
generalization of Bresenham's line algorithm. The algorithm can be further generalized to conic sections. This algorithm draws all eight octants simultaneously,...
14 KB (2,644 words) - 21:58, 8 August 2024
the sky over the course of a year Infinity symbol Lemniscates as generalized conics Lorenz attractor, a three-dimensional dynamic system exhibiting a...
9 KB (1,096 words) - 00:03, 14 August 2024
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...
15 KB (2,331 words) - 02:28, 23 September 2023
Eccentricity (mathematics) (category Conic sections)
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...
11 KB (1,318 words) - 21:06, 21 August 2024
Focus (geometry) (category Conic sections)
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...
10 KB (1,424 words) - 22:19, 18 October 2023
Bézier curve (redirect from Conic Bezier curve)
animation. Bézier curves can be combined to form a Bézier spline, or generalized to higher dimensions to form Bézier surfaces. The Bézier triangle is...
50 KB (6,966 words) - 17:04, 18 July 2024
Analytic geometry (section Conic sections)
intersecting conics to solve cubics had been used earlier by Menaechmus, Archimedes, and Alhazan, but Omar Khayyam took the praiseworthy step of generalizing the...
40 KB (5,612 words) - 00:31, 8 July 2024
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...
17 KB (1,639 words) - 22:06, 21 August 2024
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...
22 KB (3,676 words) - 13:31, 11 January 2024
Pole and polar (section General conic sections)
be generalized from circles to other conic sections which are the ellipse, hyperbola and parabola. This generalization is possible because conic sections...
12 KB (1,353 words) - 12:05, 19 July 2024
Pencil (geometry) (redirect from Pencil of conics)
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...
19 KB (2,599 words) - 12:06, 20 September 2023
transform) Tomography Tomographic reconstruction Discrete tomography Generalized conic Gardner, R.J., Geometric Tomography, Cambridge University Press, Cambridge...
2 KB (166 words) - 01:45, 19 July 2023
Pascal's theorem (category 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...
17 KB (2,193 words) - 00:12, 23 June 2024
Spieker circle (section Spieker conic)
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...
7 KB (769 words) - 22:36, 28 January 2024
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...
5 KB (470 words) - 12:49, 18 March 2024
Non-Desarguesian plane (section Conics and ovals)
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...
10 KB (1,174 words) - 02:55, 8 February 2024
Apostol and Mamikon, has been praised for its originality and clarity. Generalized conic Visual calculus "Mamikon's Proof of the Pythagorean Theorem". Wolfram...
4 KB (277 words) - 01:40, 27 June 2024
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...
10 KB (1,469 words) - 01:13, 5 May 2024
Sphere (section Spherical conics)
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...
41 KB (5,328 words) - 17:48, 16 August 2024