
	Where results make sense

Topic: Dandelin spheres

Related Topics

Directrix

Sphere

Germinal Dandelin

Stereographic projection

Conic section

Ellipse

Focus (geometry)

Matrix representation of conic sections

Quadratic function

List of mathematical theorems

Quadric

Cartesian coordinate system

Southern Pines, North Carolina

Spheroid

Geometry

In the News (Fri 17 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Dandelin spheres - Wikipedia, the free encyclopedia
		An ellipse has two Dandelin spheres, both touching the same nappe of the cone.
		A hyperbola has two Dandelin spheres, touching opposite nappes of the cone.
		The point at which the sphere touches the plane is a focus of the conic section.
	en.wikipedia.org /wiki/Dandelin_spheres (389 words)

	Germinal Pierre Dandelin - Wikipedia
		Nella matematica viene ricordato per il teorema sulle sfere di Dandelin riguardante le sezioni coniche e per il metodo di Dandelin-GrÃ¤ffe per la soluzione numerica delle equazioni algebriche.
		I primi interessi scientifici di Dandelin riguardano la geometria e nel 1822 scopre il teorema sulle sfere associate alle sezioni coniche.
		Dandelin ha fornito contributi anche alla proiezione stereografica, alla statica, all' algebra e alla teoria della probabilitÃ .
	it.wikipedia.org /wiki/Germinal_Pierre_Dandelin (304 words)

	teorema di Dandelin (Site not responding. Last check: 2007-11-02)
		DANDELIN THEOREM: "Two spheres are inscribed in a right cone and tangent to a plane p if the angle t of the cone is different from the angle f between the axis of the cone and the plane p.
		The contact points of the spheres with the plane p are called foci of the conic section.
		The straight line intersection of the plane p and the plane on which lies the circle made by contact points of the sphere with the cone, is named directrix corresponding to the focus- contact point between the sphere and the plane p.
	www.museo.unimo.it /labmat/dandin.htm (180 words)

	Dandelin
		Dandelin studied at Ghent, then in 1813 he entered the École Polytechnique in Paris.
		Dandelin has an important theorem on the intersection of a cone and its inscribed sphere with a plane, discovered in 1822, named after him.
		Among the honours which Dandelin received was election to the Royal Academy of Sciences in Brussels in 1825.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Dandelin.htm (375 words)

	Monsieur Dandelin
		Depending on the position of the spheres and the cutting plane with respect to the conic section, one can easily comprehend (when one sees the picture) why the sum/difference of the distance between any given point on the conic curve and the two focal points are constant.
		Essentially, Dandelin employs generators of hyperboloids to establish a concrete relation between the conic section, the cutting plane, and the sides of the hexagon concerned.
		Dandelin, being a military mining engineer seems to have an elegant and unique style of arriving at the geometrical theorem he worked on.
	www.cs.ubc.ca /~tzupei/Math (2167 words)

	Sfere di Dandelin - Wikipedia
		Una sfera di Dandelin tocca sia il piano che il cono in un solo punto.
		Un' ellisse possiede due sfere di Dandelin, entrambe tangenti alla stessa falda del cono.
		Una iperbole ha due sfere di Dandelin che toccano le falde oposte del cono.
	it.wikipedia.org /wiki/Sfere_di_Dandelin (430 words)

	Hyperbola (Site not responding. Last check: 2007-11-02)
		Analytically, it is defined as the set of all points for which the difference in the distance to two fixed points (called the foci) is constant.
		For a simple geometric proof that the two charaterizations above are equivalent to each other, see Dandelin spheres.
		It can also be defined as the locus of points for which the ratio of the distances to one focus and to a line (called the directrix) is a constant larger than 1.
	www.serebella.com /encyclopedia/article-Hyperbola.html (452 words)

	Dandelin spheres (Site not responding. Last check: 2007-11-02)
		In geometry, a nondegenerate conic section formed by a plane intersecting a cone has one or two Dandelin spheres characterized thus: : Each Dandelin sphere touches, but does not cross, both the plane and the cone.
		NPpharm Producer of sugar spheres, neutral pellets, globules, mcc spheres.
		Platonic Spheres The five regular polyhedra mapped onto the surface of their surrounding spheres, which can be rotated in java applets.
	www.serebella.com /encyclopedia/article-Dandelin_spheres.html (449 words)

	Applet JDandelin (Site not responding. Last check: 2007-11-02)
		He emloys spheres inscribed to a cone which touch the intersecting plane in two points which are foci of the conic section.
		The upper sphere touches the surface of the cone from inside in a circle — call it k — and it also touches the intersecting plane from above at a point F. Similarly the lower sphere is also inscribed to the conical surface from inside and touches it in a circle k'.
		Its center is at point C situated below the cone vertex V. The sphere touches the surface of the cone from inside in a circle k and it also touches the intersecting plane at a point F. In addition to the intersecting plane there is also another plane displayed on the image.
	www.lostlecture.host.sk /JDandelinEn.htm (1671 words)

	Dandelin (Site not responding. Last check: 2007-11-02)
		During Napoleon's time back in control of France, Dandelin worked at the Ministry of the Interior under the command of Carnot.
		In 1826 he generalised his theorem to a hyperboloid of revolution, rather than a cone, relating Pascal 's hexagon, Brianchon 's hexagon and the hexagon formed by the generators of the hyperboloid.
		The history of the Dandelin- Gräffe method is discussed in [2] and [5].
	www-history.mcs.st-and.ac.uk /~history/Mathematicians/Dandelin.html (422 words)

	KöMaL - Rita Kós: Conics and Dandelin spheres
		KöMaL - Rita Kós: Conics and Dandelin spheres
		By intersecting a cone with a plane - not passing through the vertex of the cone -, curves of different types can be obtained, depending on the angle enclosed between the plane and the axis of the cone.
		In 1822, he discovered the relation between the intersection curve of the cone with a plane, the foci of the intersecion conics, and the two inscribed spheres touching the cone and the intersecting plane.
	www.komal.hu /cikkek/dandelin/dandelin.e.shtml (225 words)

	Ellipse - Wikipedia, the free encyclopedia
		An ellipse is a type of conic section : if a cone is cut with a plane which does not intersect the cone's base, the intersection of the cone and plane is an ellipse.
		For a short elementary proof of this, see Dandelin spheres.
		The size of an ellipse are determined by two constants, conventionally denoted a and b.
	en.wikipedia.org /wiki/Ellipse (966 words)

	Dandelin (Site not responding. Last check: 2007-11-02)
		Germinal Dandelin 's father, who was an administrator, was French but his mother came from Hainaut, now in Belgium.
		From 1835 he was in the Belgium army, assigned posts in charge of building fortifications in Namur, Liège and, later, in Brussels.
		Dandelin's early mathematical influence was Quetelet, who was two years younger than him, and his early interests were in geometry.
	www-groups.dcs.st-and.ac.uk /%7Ehistory/Mathematicians/Dandelin.html (422 words)

	Spheres
		Blue Spheres Blue Spheres is the game created by locking on Sonic & Knuckles; to Sonic the Hedgehog 3 and Sonic & Knuckl...
		Celestial spheres The celestial spheres relate to phenomena and ruled by a divine force.
		Dandelin spheres In conic section formed by a plane intersecting a cone has one or two Dandelin spheres characterized th...
	www.brainyencyclopedia.com /topics/spheres.html (67 words)

	[No title]
		(labeled so that f1 is closer to v1) (this is where the Dandelin spheres touches the cutting plane) (if it is a parabola, f2 and v2 are at Infinity) Let c0 be the center of the conic section.
		(tangent circle is the intersection of the cone and the Dandelin spheres) Let j1 be a point on the smaller tangent circle nearest to v1.
		Let s1j1 and s2j2 be the radii of the first and second Dandelin spheres.
	www.ciram.unibo.it /~irrsae/coniche/Xah/Conicsections/conicsMath.ma (1051 words)

	Encyclopedia: Dandelin spheres
		Updated 157 days 18 hours 13 minutes ago.
		The reason for interest in Dandelin spheres is this theorem:
		Dandelin Spheres page by Hop David ( http://www.clowder.net/hop/Dandelin/Dandelin.html)
	www.nationmaster.com /encyclopedia/Dandelin-spheres (435 words)

	Sphere (Site not responding. Last check: 2007-11-02)
		Plane is tangent to the sphere, a point).
		Angles for random rotation of a sphere is
		Sphere is to generate three gaussian random variables
	www.math.sdu.edu.cn /mathency/math/s/s556.htm (349 words)

	Dandelin's Spheres (PRIME)
		Evidently, as we would expect, the tangent curve between a sphere and a cone is a circle, one whose every point is equidistant from the vertex of the cone.
		We then inscribe two spheres in the cone, one above and one below the ellipse, so that they are each tangent to the sphere and to the plane of the ellipse simultaneously.
		Students should try a quick sketch of these other two cases, to ensure that the logic of their proofs is transparent.Here, in Dandelin’s elegantly simple constructions, we find the deepest harmony between our spatial intuitions and the formalisms of Euclidean geometry.
	mathacademy.com /pr/prime/articles/dandelin/index.asp?...&PRE=,aaa (690 words)

	Ellipse - free-definition (Site not responding. Last check: 2007-11-02)
		An ellipse can also be characterized as the intersection of a cone with a suitably situated plane; that is why the term conic section is used.
		For a short elementary proof of the equivalance of these two characterizations, see Dandelin spheres.
		If the two foci coincide, then the ellipse becomes a circle; depending on context, a circle may or may not be considered a type of ellipse.
	www.free-definition.com /Ellipse.html (806 words)

	Ellipse [Definition] (Site not responding. Last check: 2007-11-02)
		For a short elementary proof of this, see Dandelin spheres In geometry, a nondegenerate conic section formed by a plane intersecting a cone has one or two Dandelin spheres characterized thus: Each Dandelin sphere touches, but does not cross, both the plane and the cone.
		The size and shape of an ellipse are determined by two constants, conventionally denoted a and b.
		Namely, given a surface lying in R3, the Gauss map is a continuous map such that is orthogonal to S at p....
	www.wikimirror.com /Ellipse (2621 words)

	KöMaL - Rita Kós: Conics and Dandelin spheres
		Let P be an arbitrary point of the conic section.
		Consider the two spheres which touch the cone and the plane.
		We can use the spheres to prove another important property of the ellipse.
	www.komal.hu /cikkek/dandelin/ellipszis.e.shtml (184 words)

	Germinal Pierre Dandelin
		He is the eponym of the Dandelin spheres, of Dandelin's theorem in geometry (for an account of that theorem, see Dandelin spheres), and of the Dandelin-Gräffe numerical method; of solution of algebraic equations.
		A S Householder, Dandelin, Lobachevskii, or Gräffe?, Amer.
		A Quetelet, G P Dandelin, Biographie nationale XIV (Brussels,1873), 663-668.
	brainyencyclopedia.com /encyclopedia/g/ge/germinal_pierre_dandelin.html (214 words)

	Dandelin spheres (Site not responding. Last check: 2007-11-02)
		This concept is named in honor of Germinal PierreDandelin.
		An ellipse has two Dandelin spheres, both touching the same nappe of thecone.
		A hyperbola has two Dandelin spheres, touching opposite nappes of thecone.
	www.therfcc.org /dandelin-spheres-206482.html (343 words)

	Dandelin
		Much of Dandelin's demonstrations rests on the fact that two of a sphere's tangent line segments
		A pair of Dandelin spheres define two tangent cones:
		They also define two sets of cutting planes which are tangent planes to either the thin or fat cone.
	www.clowder.net /hop/Dandelin/Dandelin.html (580 words)

	Conic section - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-02)
		In projective geometry, the conic sections in the projective plane are equivalent to each other up to projective transformations.
		See Dandelin spheres for a short elementary argument showing that the characterization of these curves as intersections of a plane with a cone is equivalent to the characterization in terms of foci, or of a focus and a directrix.
		Let there be a cone whose axis is the z -axis.
	xahlee.org /_p/wiki/Conics.html (1353 words)

	KöMaL - Rita Kós: Conics and Dandelin spheres
		Let P be an arbitrary point of the conic.
		Consider the sphere G which touches the plane of the conic and the cone at the point F and at circle k, respectively.
		Let the generator through P intersect k at point P'.
	www.komal.hu /cikkek/dandelin/parabola.e.shtml (131 words)

	Hyperbola -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-02)
		Geometrically, it is defined as the intersection between a (Cone-shaped mass of ovule- or spore-bearing scales or bracts) cone and a (A carpenter's hand tool with an adjustable blade for smoothing or shaping wood) plane which cuts through both halves of the cone.
		For a simple geometric proof that the two characterizations above are equivalent to each other, see (Click link for more info and facts about Dandelin spheres) Dandelin spheres.
		(Click link for more info and facts about Dandelin spheres) Dandelin spheres
	www.absoluteastronomy.com /encyclopedia/h/hy/hyperbola.htm (450 words)

	Eccentric.html
		He has a lot of information on these beautiful curves.
		Look for his explanation of Dandelin spheres, they give insight.
		Here is a paragraph on eccentricity Xah wrote:
	www.clowder.net /hop/Eccentric.html (209 words)

	SPHERE WATER FOUNTAIN STONE SCULPTURE AS WATER FEATURE FOR LANDSCAPE (Site not responding. Last check: 2007-11-02)
		SPHERE WATER FOUNTAIN STONE SCULPTURE AS WATER FEATURE FOR LANDSCAPE
		fountain, water feature, sphere, ball fountain, water fountains, fountains, water, ponds, art, sculpture, monument, sculptures, floating spheres, granite, custom, landscape, architect, bronze, foggers, feng shui, new age, corporate gift, carving, sculptor, stone sculptures, waterfountain, waterfountains, Los Angeles, California, ball, office buildings, golf
		The sphere fountain is ideal for exterior Landscape designs and interior applications, both commercial and residential, with custom designed bases available to meet your special needs.
	www.waterfountains.com (96 words)

	eBay Store - Madagascar Minerals: Ammonite Products, Wholesale Products, Orbicular Jasper Products (Site not responding. Last check: 2007-11-02)
		SPECTACULAR Clear Quartz Crystal Sphere - HEALING Ball
		WHITE AMMONITE FOSSIL - SET of 5
		STAR ROSE QUARTZ SPHERE SET of 4
	stores.ebay.com /Madagascar-Minerals (307 words)

Try your search on: Qwika (all wikis)