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Topic: Germinal Dandelin

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	Germinal Pierre Dandelin - Wikipedia, the free encyclopedia
		Germinal Pierre Dandelin (April 12, 1794 - February 15, 1847) was a mathematician, soldier, and professor of engineering.
		He was born near Paris to a French father and Belgian mother, studying first at Ghent then returning to Paris to study at the École Polytechnique.
		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.
	en.wikipedia.org /wiki/Germinal_Dandelin (215 words)

	Dandelin spheres - Wikipedia, the free encyclopedia
		Dandelin spheres—graphics by Hop David, used by permission
		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.
	en.wikipedia.org /wiki/Dandelin_spheres (392 words)

	Dandelin biography
		Germinal Dandelin's father, who was an administrator, was French but his mother came from Hainaut, now in Belgium.
		Dandelin's early mathematical influence was Quetelet, who was two years younger than him, and his early interests were in geometry.
		Dandelin has an important theorem on the intersection of a cone and its inscribed sphere with a plane, discovered in 1822, named after him.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Dandelin.html (439 words)

	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.
		Germinal Pierre Dandelin (1794-1847) was a French engineer, who lived in Belgium.
		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)

	Applet JDandelin (Site not responding. Last check: 2007-10-30)
		In addition it gives you a chance to see and understand the famous Dandelin's proof of the fact that the ellipse parabola and hyperbola are conic sections.
		Germinal Pierre Dandelin was a mathematician of French-Belgium origin.
		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.
	www.lostlecture.host.sk /JDandelinEn.htm (1671 words)

	Monsieur Dandelin
		Germinal Dandelin (1794-1847) was a mathematician whose career was very much influenced by the political upheavals of his time.
		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 (2165 words)

	Mathematics at West Point in the Early Twentieth Century
		At the Cavalry School at Moravian Weisskirchen Echols, observed the instructor use a model of the cone to explain Dandelin's proof that a section of a cone is an ellipse.
		Germinal Pierre Dandelin (1794-1847) discovered his proof using spheres in a cone to prove that a plane intersecting a cone is a conic.
		Dandelin was a student at the Ecole Polytechnique and one must wonder how his study of descriptive geometry influenced his discovery of this proof.
	www.dean.usma.edu /departments/math/people/rickey/dms/talks/2004-02-19-Early20th-PASHoM.htm (6354 words)

	Dandelin spheres
		If a cone is sliced through by a plane, the two spheres that just fit inside the cone, one on each side of the plane and both tangent to it and touching the cone, are known as Dandelin spheres.
		They are named after the Belgian mathematician and military engineer Germinal Pierre Dandelin (1794-1847) who gave an elegant proof that the two spheres touch the conic section at its foci.
		In 1826, Dandelin showed that the same result applies to the plane sections of a hyperboloid of revolution.
	www.daviddarling.info /encyclopedia/D/Dandelin_spheres.html (159 words)

	Xah: Special Plane Curves: Conic Sections
		Many later mathematicians have also made contribution to conics, espcially in the development of projective geometry where conics are fundamental objects as circles in Greek geometry.
		Dandelin sphere is a sphere of certain size and position inscribed inside the cone.
		Dandelin sphere relate many properties of the conics to the cone.
	xahlee.org /SpecialPlaneCurves_dir/ConicSections_dir/conicSections.html (1861 words)

	Dandelin
		Dandelin studied at Ghent, then in 1813 he entered the École Polytechnique in Paris.
		During Napoleon's time back in control of France, Dandelin worked at the Ministry of the Interior under the command of
		He gave a method of approximating the roots of an algebraic equation, now named the Dandelin-
	www.educ.fc.ul.pt /icm/icm2003/icm14/Dandelin.htm (373 words)

	[No title] (Site not responding. Last check: 2007-10-30)
		There are many proofs known, but one of the most attractive is due to the nineteenth century Belgian mathematician Germinal Dandelin.
		The three-dimensional proof of Pascal's Theorem is now well known, but seems to have originated with Dandelin.
		Dandelin's three-dimensional proof of Pascal's Theorem (and its dual, Brianchon's Theorem) is contained in the paper
	www.math.ubc.ca /~cass/courses/java/pascal/pascal.html (355 words)

	Tales of Statisticians \| Adolphe Quetelet
		He apprenticed to a painter, turned out acceptable paintings of his own, wrote poetry, and with his friend and fellow Franco-Belgian Germinal Dandelin, collaborated on an opera.
		In 1819, Quetelet received its first doctoral degree, for a thesis on the focal curve (a result improved on in 1822 by his no less versatile operatic collaborator Dandelin).
		In October of that year, equipped with this new distinction, he became a professor in Brussels, the city where he was to live for the rest of his life.
	www.umass.edu /wsp/statistics/tales/quetelet.html (1596 words)

	Dandelin's Spheres (PRIME)
		This article presents a now classic proof, due to the French/Belgian mathematician Germinal Dandelin (1794 –; 1847), which shows the equivalence of these definitions.
		To show that they are, Dandelin peformed an ingenious construction.
		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.
	www.mathacademy.com /pr/prime/articles/dandelin/index.asp (689 words)

	WhoWasThere reply
		George Green was 47 this year and would die the following year.
		Germinal P Dandelin was 46 this year and would die in a further 7 years.
		Franz Adolph Taurinus was 46 this year and would die in a further 34 years.
	www-history.mcs.st-and.ac.uk /history/cgi-bin/mathyear.cgi?YEAR=1840 (3678 words)

	Geometer Definition / Geometer Research (Site not responding. Last check: 2007-10-30)
		Germinal DandelinGerminal Pierre Dandelin (1794 - 1847) was a mathematician, soldier, and professor of engineering.
		He was born near Paris, where he studied at the École Polytechnique.
		[click for more] -- Dandelin spheres in conic sections
	www.elresearch.com /Geometer (1171 words)

	Math Forum Discussions
		Hi, I'd really appreciate it if someone can tell me how Germinal
		Pierre Dandelin generalized his theorem on conics to a
		Dandelin to relate Pascal's hexagon, Brianchon's hexagon and the
	mathforum.org /kb/thread.jspa?threadID=24924&messageID=67992 (77 words)

	nrich.maths.org::Mathematics Enrichment::Conic Sections
		The key question now is how these plain plane conic section developments are reconciled with the original Greek version.
		The following justification of their equivalence is based on ideas first conceived by Germinal Dandelin in 1822 and are some of my favourite bits of mathematics.
		The idea behind the above complicated looking diagrams is absolutely amazing and it is well worth putting in the effort to work out what is going on.
	www.nrich.maths.org.uk /public/viewer.php?obj_id=1486&part=index&refpage=monthindex.php (1834 words)

	Abstracts For Grad Student Seminar - Winter 1998
		His actual proof, unfortunately, will never be known but how he might have arrived at his result is suggested by Germinal Dandelin's elegant illustration of Pascal's Theorem.
		In this presentation, we will explain Dandelin's reasoning with the help of a sequence of pictures drawn in PostScript.
		We hope these pictures will clearly demonstrate Dandelin's ideas which proves Pascal's theorem requiring neither analytic geometry nor messy calculations.
	www.iam.ubc.ca /activities/abstracts_98w.html (1771 words)

	[No title]
		More generally, an n-dimensional cube in the first quadrant of a Euclidean space with one vertex at the origin is given by the collection of all n-tuples of the form
		A proof by the 17th century French mathematician Germinal Dandelin of the equivalence of the plane geometry and conic section definitions of the ellipse, parabola, and hyperbola.
		Given a space X and a subset A of X, we say that A is dense if the intersection of every open set of X with A is non-empty.
	www.mathacademy.com /platonic_realms/encyclop/main.txt (8404 words)

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