
	Where results make sense

Topic: Conic

Related Topics

Quadratic function

Parabola

In the News (Sun 27 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Conic section - Wikipedia, the free encyclopedia
		The conic sections were named and studied as long ago as 200 BC, when Apollonius of Perga undertook a systematic study of their properties.
		The semi-latus rectum of a conic section, usually denoted l, is the distance from the single focus, or one of the two foci, to the conic section itself, measured along a line perpendicular to the major axis.
		Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest.
	en.wikipedia.org /wiki/Conic_section (1393 words)

	CONIC SECTION - LoveToKnow Article on CONIC SECTION (Site not responding. Last check: 2007-11-05)
		One definition, which is of especial value in the geometrical treatment of the conic sections (ellipse, parabola and hyperbola) in piano, is that a conic is the locus of a point whose distances from a fixed point (termed the focus) and a fixed line (the directrix) are in constant ratio.
		A conic may also be regarded as the polar reciprocal of a circle for a point; if the point be without the circle the conic is an ellipse, if on the circle a parabola, and if within the circle a hyperbola.
		In analytical geometry the conic is represented by an algebraic equation of the second degree, and the species of conic is solely determined by means of certain relations between the coefficients.
	5.1911encyclopedia.org /C/CO/CONIC_SECTION.htm (3749 words)

	PlanetMath: conic section
		In Euclidean 3-space, a conic section, or simply a conic, is the intersection of a plane with a right circular double cone.
		The margin of the shadow of the ball is a conic, the ball is one of the Dandelin spheres of that conic, and the ball meets the table at the focus corresponding to that sphere.)
		To work with conic sections in such an astronomical context, it is very useful to have a description in terms of polar coordinates centered at one focus.
	planetmath.org /encyclopedia/ConicSection.html (872 words)

	History of Conic Sections (Site not responding. Last check: 2007-11-05)
		Conic sections are some of the oldest and most studied curves their history stretches to 300 BC.
		The conics were defined as the intersections of a plane with a double-napped circular cone.
		Appollonius was the first to base the theory of all three conics on sections of one circular cone and was the person to give them the names ellipse, parabola, and hyperbola.
	www.bath.ac.uk /~ma3hrt/History.html (301 words)

	Map Projections: Conic Projections
		Due to simple construction and inherent distortion pattern, conic projections have been widely employed in regional or national maps of temperate zones (while azimuthal and cylindrical maps were favored for polar and tropical zones, respectively), especially for areas bounded by two not too-distant meridians, like Russia or the conterminous United States.
		Relatively few projections are called "conic"; nevertheless, many others are ruled by conic principles, since the cone is a limiting case of both the circle (a cone with no height, and cone constant 1) and the cylinder (a cone with vertex at infinity, with standard parallels symmetrical north and south of the Equator).
		In a particular case of Albers's conic projection, either 90°N or 90°S is chosen as a standard parallel, and therefore meridians converge at a pole.
	www.progonos.com /furuti/MapProj/Normal/ProjCon/projCon.html (1484 words)

	Conic section parameterization
		The conic curves are: ellipses, circles, parabolas, and hyperbolas.
		Since the conic is degree 2 and the line is degree 1, they intersect in at most two points.
		That conic section is the intersection of a plane through the vertex of the cone, (0,0,0), and results in a point (degenerate ellipse), line (degenerate parabola), or a pair of intersecting lines (degenerate hyperbola).
	www.science.gmu.edu /~jsteidel/806-prj/project.html (1765 words)

	Conic sections (Site not responding. Last check: 2007-11-05)
		If a cylinder is sliced by a plane a number of curves arise depending on the angle of the plane with respect to the cylinder axis, these are called conic sections.
		Conic sections were studied extensively by the Greeks as early as 350 BC in an attempt to solve the great geometric problems of the day, namely, squaring the circle, duplicating the cube, and trisecting an angle.
		Note that in general if a conic section is stretched along an axis other than a principle axis then the resulting curve is no longer a conic section.
	astronomy.swin.edu.au /~pbourke/curves/conic (339 words)

	AllRefer.com - conic section (Mathematics) - Encyclopedia
		conic section or conic[kon´ik] Pronunciation Key, curve formed by the intersection of a plane and a right circular cone (conical surface).
		The ordinary conic sections are the circle, the ellipse, the parabola, and the hyperbola.
		When the plane passes through the vertex of the cone, the result is a point, a straight line, or a pair of intersecting straight lines; these are called degenerate conic sections.
	reference.allrefer.com /encyclopedia/C/conicsec.html (199 words)

	Numbers: Quadratic Relations & Conic Sections
		Conic sections arise from the study of the intersection between a plane and a cone, specifically a double-napped cone.
		Conic sections are also known as quadratic relations because the equations which describe them are second order and not always functions.
		These conic sections are excellent mathematical models of the paths taken by planets, meteors, spacecrafts, light rays, and many other objects.
	www.andrews.edu /~calkins/math/webtexts/numb19.htm (2067 words)

	Jim King's Conic Macros
		Given the points F1 and F2 which are the foci and a point P on the conic, one macro constructs the ellipse through P with these foci and another constructs the hyperbola with the same foci.
		One constructs a conic when two of the 5 points "coincide"; in other words one is given 4 points A, B, C, D and a line d through D which is to be a tangent line through the conic (so D is a double point).
		Given a conic the foci and the axes of symmetry are constructed.
	mathforum.org /dynamic/submissions/kingconicmacros/index.html (760 words)

	Conic Sections in Ancient Greece
		Menaechmus is credited with the discovery of conic sections around the years 360-350 B.C.; it is reported that he used them in his two solutions to the problem of "doubling the cube".
		Neugebauer suggests that the origin of the concept is in the theory of sundials, since the sheaf of light rays involved in the design of sundials is a cone which is cut by the plane of the horizon in a hyperbola, and a portion of that hyperbola is then marked out on the sundial.
		Conic Sections continues to define a diameter to be a straight line bisecting each of a series of parallel chords of a section of a cone.
	www.math.rutgers.edu /~cherlin/History/Papers1999/schmarge.html (5833 words)

	Analysis of conic sections
		A conic section is the intersection of an extended cone and a plane.
		The general conic equation may represent a standard conic section that has been translated and rotated.
		To convert the general equation to a standard form, a rotation and a translation are applied to give a new set of coefficients for the equation the conic section that does not change its shape.
	home.att.net /~srschmitt/conic_eqn_analysis.html (1097 words)

	Curves in 3D
		The focal conics E and H can be viewed as degenerate members of the family Q, where µ = 0 and µ = -b², respectively.
		conics": A pair of plane conics that lie in perpendicular plane and such that each passes trough the foci of the other.
		N.B.: The angles between the tangent at e and either part of the string from h through e to h0 are equal, i.e., together the focal conics have a reflection property.
	www.lems.brown.edu /vision/people/leymarie/Notes/CurvSurf/Curves.html (475 words)

	conic section
		A conic section is an algebraic curve of the 2nd degree (and every 2nd degree equation represents a conic).
		The conic section can be defined as the collection of points P for which the ratio 'distance to F / distance to l' is constant.
		A conic section is used, together with a hexagon, to show Pascal's theorem (or its dual, Brianchon's theorem).
	www.2dcurves.com /conicsection/conicsection.html (403 words)

	Degenerated conic sections and classification
		The conic section who is degenerated in these lines has the equation (ux + vy)(u'x + v'y) = 0.
		The line DP is a component of the conic section and thus the conic section is degenerated.
		If P' does not exist, the conic section is degenerated in two coinciding lines and D is double point.
	www.ping.be /~ping1339/ontaard.htm (849 words)

	Constructing conic sections (Site not responding. Last check: 2007-11-05)
		It illustrates that the "locus definitions" of the conic sections can actually be used to construct the conic sections.
		A natural extension to the geometric constructions is the derivation of the quadratic equations for the conics from the locus definitions.
		Each of the animations for constructing the conic sections, parabla, ellipse and hyperbola, is available in a larger form by clicking on big-conic.
	astro.temple.edu /~dhill001/conic_via_locus (1051 words)

	Conic Section Gallery (Site not responding. Last check: 2007-11-05)
		The following is a gallery of demos for illustrating selected families of conic sections These figures and animations can be used by instructors in a classroom setting or by students to aid in acquiring a visualization background relating to the change of parameters in expressions.
		The conic sections are the non-degenerate curves generated by the intersections of a plane with one or two cones in the double cone as pictured below.
		At http://math2.org/math/algebra/conics.htm is a discussion of conic sections generated by intersecting a double cone with detailed descriptions of the cases including degenerate cases.
	mathdemos.gcsu.edu /family_of_functions/conic_gallery.html (781 words)

	Conic Sections (Site not responding. Last check: 2007-11-05)
		Ellipse is known by its focal definition: it's a locus of all points P in the plane the sum of whose distances from two fixed points F
		That such a simple proof of the result known yet to ancient Greeks was discovered in the 19th century is nothing short of wonderful.
		The border of the shadow is liable to be one of the three conic sections.
	www.cut-the-knot.com /proofs/conics.html (594 words)

	Applet JDandelin (Site not responding. Last check: 2007-11-05)
		In 1822 he introduced his elegant proofs of the fact that ellipse, hyperbola and parabola are produced as an intersection of a cone with a plane.
		He emloys spheres inscribed to a cone which touch the intersecting plane in two points which are foci of the conic section.
		It means that the distance of arbitrary point P of the investigated curve from point F is equal to its distance from line p.
	www.lostlecture.host.sk /JDandelinEn.htm (1671 words)

	conicsections
		This investigation of conic sections using the World Wide Web, as a source of information, practice and testing will be a different way of approaching the topic and I hope a more enjoyable experience for the student.
		They will write a paragraph explaining how the conic section is used in the situation they choose. The paper will consist of six paragraphs, one introductory paragraph, four paragraphs concerning the conic sections, and one paragraph concluding the paper. A copy of the paper will be submitted in the students' portfolio.
		The chapter on conic sections in the book is very difficult for the students to grasp due to the numerous formulas and similarities between the figures.
	www.geocities.com /kimandreassi/conicsections.html (2955 words)

	CONICS... Habitat for the 21st Century
		Arena Conic will be up through the July 4th celebration and beyond and then moved to the Black Rock Desert for Burning Man 2004 and erected for a third time as an art exibition.
		Conics built in the early 1970's are still used as living spaces in the hills of Mendocino County California and elsewhere in the Pacific Northwest.
		Conics can withstand impacts from falling objects (by virtue of its trampoline-like flexibility), yet Conics remain very stable, deforming only when necessary, and quickly returning to the original shape.
	www.fishrock.com /conics (1250 words)

	Adam Coffman --- Conics
		If two conics in a linear system are disjoint, then every pair of conics in the linear system will also be disjoint, and there are no base points.
		This corresponds to the geometric definition of a conic section as the intersection of a cone (defined by the homogeneous equation in xyz-space) with a plane (defined by z = 1).
		To see how I rendered the conic sections in the picture to the left, Click Here to see a "side view," showing the cones in xyz-space, whose intersection with the plane z=1 (the top of the box) is shown in the two-dimensional figure.
	www.ipfw.edu /math/Coffman/pov/lsoc.html (1223 words)

	UM-VRL: Conic Sections (Site not responding. Last check: 2007-11-05)
		If the plane passes through the tip of the cone, so-called degenerated conic sections (a point, a line, or two intersecting lines) are obtained.
		Conic sections have been studied for over 2000 years and are still important tools for present-day investigations in science, engineering, and other areas.
		All types of conic sections, including the degenerated cases, can be produced.
	www-vrl.umich.edu /sel_prj/ibm/cone (395 words)

	Historical View of the Conic Sections
		In this hypertext, we consider the conic sections, which have been studied for over 2000 years.
		Apollonius of Perga, one of the greatest Greek mathematicians of the time (circa 200 B.C.), appears to have been the first to have rigorously studied the conic sections.
		More information on Apollonius, as well as many other mathematicians, is held at the MacTutor History of Mathematics Archive at the University of St. Andrews.
	www.krellinst.org /UCES/archive/resources/conics/node5.html (438 words)

	Conic Hill walking, close to balmaha in Stirlingshire's eastern side of Loch Lomond
		A cracking little climb, which I done on a February day (2003), and is just 20 minutes from Glasgow can be found just outside Balmaha on the eastern shore of Loch Lomond, Stirlingshire.
		The hill is of course, Conic Hill, some 358 metres from sea level.
		For those of you out there, who are new to the noble art of hillwalking / mountain climbing, Conic Hill and Ben A'n, on my Trossachs page, are ideal starting points or learning curves for an enjoyable, slightly addictive hobby.
	www.conneryscottishwalks.co.uk /conichill.html (298 words)

Try your search on: Qwika (all wikis)