21. SAPERE.it - Conica Translate this page dandelin, germinal-Pierre - Desargues, Gérard - diàmetro - diametrale - direttrice -eccentricità - ellisse - focale - fuòco - invariànte - ipèrbole http://www.sapere.it/gr/ArticleViewServletOriginal?otid=GEDEA_conica

22. Monsieur Dandelin I was first introduced to Monsieur germinal Pierre dandelin in Math 309, germinal dandelin (17941847) was a mathematician whose career was very much http://www.cs.ubc.ca/~tzupei/Math/

Monsieur Dandelin and his 3D proof of Pascal's Theorem Welcome to my Monsieur Dandelin's page! http://www.adobe.com ). You might also want to pre-read the English translation of Germinal Dandelin's "Hyperboloids of Revolution and the Hexagons of Pascal and Brianchon" in order to make any sense out of the illustrations I made. Short cuts: How did I find out about Monsieur Dandelin and how I reacted to his work. Who is Dandelin? What's Pascal's Theorem? What's Brianchon's Theorem? ... Three basic concepts in Dandelin's hyperboloid model List of illustrations: picture 1 picture 2 picture 3 picture 25 ... More info How did I find out about Monsieur Dandelin and how I reacted to his work I was first introduced to Monsieur Germinal Pierre Dandelin in Math 309, 1997 Spring by Prof. Bill Casselman . We were studying astronomical math and Dandelin's 3D proof of conic sections properties was a perfect sculpture to initiate our interest. The 3D proof involves a cone with one or two spheres inscribed inside and a cutting plane. 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. (If you are interested in reading more about this, please refer to Xah's conic section page Intrigued by Dandelin's unique geometric approach, I got hold of a copy of his papers

23. Dandelin's Spheres (PRIME) The famous construction of dandelin, from the Platonic Realms Interactive Math due to the French/Belgian mathematician germinal dandelin (1794 – 1847), http://www.mathacademy.com/pr/prime/articles/dandelin/index.asp

BROWSE ALPHABETICALLY LEVEL: Elementary Advanced Both INCLUDE TOPICS: Basic Math Algebra Analysis Biography Calculus Comp Sci Discrete Economics Foundations Geometry Graph Thry History Number Thry Physics Statistics Topology Trigonometry lassically, conic sections (the ellipse parabola , and hyperbola ) are defined by the intersection of a plane with a cone We take the case of an ellipse; the other cases are quite similar. As a conic section, an ellipse is the intersection of a cone and a plane whose angle to the vertical is larger than that of the generator of the cone. That is, it is the curve that results when a plane slices right through one of the nappes of the cone. In plane geometry, however, an ellipse is the locus of points in the plane, the sum of whose distances from two fixed points, called the foci, remains constant. At first glance it is not obvious that these are definitions of the same mathematical object. To show that they are, Dandelin peformed an ingenious construction. call V Now draw the two tangents to the circle that intersect at V . Then the points of tangency are equidistant from V The standard proof of this fact is straightforward, but we'll content ourselves with noticing that it follows more or less immediately from the symmetry of the situation. Indeed, if we rotate the above figure about its axis of symmetry, we get an immediate extension to the case of a sphere inscribed in a cone:

24. Dandelin Spheres -- Facts, Info, And Encyclopedia Article (Click link for more info and facts about germinal Pierre dandelin) germinalPierre dandelin. Each conic section has one dandelin sphere for each focus. http://www.absoluteastronomy.com/encyclopedia/d/da/dandelin_spheres.htm

Dandelin spheres [Categories: Conic sections] In (The pure mathematics of points and lines and curves and surfaces) geometry , a nondegenerate ((geometry) a curve generated by the intersection of a plane and a circular cone) 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. This concept is named in honor of (Click link for more info and facts about Germinal Pierre Dandelin) Germinal Pierre Dandelin Each conic section has one Dandelin sphere for each focus. An (A closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it) ellipse has two Dandelin spheres, both touching the same nappe of the cone. A (An open curve formed by a plane that cuts the base of a right circular cone) hyperbola has two Dandelin spheres, touching opposite nappes of the cone. A (A plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve) parabola has just one Dandelin sphere.

25. List Of Mathematicians -- Facts, Info, And Encyclopedia Article (Click link for more info and facts about germinal Pierre dandelin) germinalPierre dandelin (France, Belgium, 1794 1847) http://www.absoluteastronomy.com/encyclopedia/l/li/list_of_mathematicians.htm

List of mathematicians [Categories: Math lists, Mathematicians, Lists of people by occupation] The famous (A person skilled in mathematics) mathematician s are listed below in (An Indo-European language belonging to the West Germanic branch; the official language of Britain and the United States and most of the Commonwealth countries) English (A character set that includes letters and is used to write a language) alphabet ical (A transcription from one alphabet to another) transliteration order (by (The name used to identify the members of a family (as distinguished from each member's given name)) surname A (Click link for more info and facts about Abu'l-Hasan al-Uqlidisi) Abu'l-Hasan al-Uqlidisi (Arab mathematician, ? - ?) (Click link for more info and facts about Abu'l-Wafa) Abu'l-Wafa (Iran, (Click link for more info and facts about 940) (Click link for more info and facts about 998) (Norwegian mathematician (1802-1829)) Niels Henrik Abel (Norway, 1802 - 1829) (Click link for more info and facts about Abraham bar Hiyya Ha-Nasi) Abraham bar Hiyya Ha-Nasi (Click link for more info and facts about Ralph H. Abraham)

26. Germinal Disc - Definition Of Germinal Disc By The Free Online Dictionary, Thesa Meaning of germinal disc. What does germinal disc mean? germinal disc synonyms,germinal disc antonyms. germinal center of Flemming germinal dandelin http://www.thefreedictionary.com/germinal disc

Domain='thefreedictionary.com' word='germinal disc' join mailing list webmaster tools Word (phrase): Word Starts with Ends with Definition subscription: Dictionary/ thesaurus Computing dictionary Medical dictionary Legal dictionary Financial dictionary Acronyms Columbia encyclopedia Wikipedia encyclopedia Hutchinson encyclopedia germinal disc Also found in: Medical 0.03 sec. Page tools Printer friendly Cite / link Email Feedback Thesaurus Legend: Synonyms Related Words Antonyms Noun germinal disc - a layer of cells on the inside of the blastula blastoderm blastodisc germinal area layer - thin structure composed of a single thickness of cells Mentioned in References in classic literature No references found No references found Dictionary/thesaurus browser Full browser Germarium Germen germfree germicidal ... germinal area germinal disc germinal disk Germinal layers Germinal membrane Germinal spot ... Germinal Dandelin germinal disc germinal disk germinal disk germinal epithelium Germinal layers ... Germinative Word (phrase): Word Starts with Ends with Definition Free Tools: For surfers: Browser extension Word of the Day NEW!

27. Germinate - Definition Of Germinate By The Free Online Dictionary, Thesaurus And germinal cell germinal center of Flemming germinal dandelin germinal disc germinal disc germinal disk germinal disk germinal epithelium http://www.thefreedictionary.com/germinate

Domain='thefreedictionary.com' word='germinate' join mailing list webmaster tools Word (phrase): Word Starts with Ends with Definition subscription: Dictionary/ thesaurus Computing dictionary Medical dictionary Legal dictionary Financial dictionary Acronyms Columbia encyclopedia Wikipedia encyclopedia ... encyclopedia germinate Also found in: Medical Columbia Wikipedia Hutchinson 0.01 sec. Page tools Printer friendly Cite / link Email Feedback ger·mi·nate (jûr m -n t v. ger·mi·nat·ed ger·mi·nat·ing ger·mi·nates v. tr. To cause to sprout or grow. v. intr. To begin to sprout or grow. To come into existence: An idea germinated in his mind. [Latin germin re , germin t- to sprout , from germen , germin- seed ; see gen in Indo-European roots.] ger mi·na tion n. ger mi·na tive adj. ger mi·na tor n. germinate germination of a bean seed Thesaurus Legend: Synonyms Related Words Antonyms Verb germinate - produce buds, branches, or germinate; "the potatoes sprouted" bourgeon burgeon forth sprout spud ... grow - increase in size by natural process; "Corn doesn't grow here"; "In these forests, mushrooms grow under the trees" germinate - cause to grow or sprout; "the plentiful rain germinated my plants"

28. List Of Scientists By Field Translate this page dandelin, germinal Pierre. dandelin, germinal Pierre. Danforth, Charles Haskell.Danforth, Charles Haskell. Daniell, John Frederic. Daniell, John Frederic http://www.indiana.edu/~newdsb/d.html

Dahlberg, Gunnar Dainelli, Giotto Dainelli, Giotto Dakin, Henry Drysdale Dakin, Henry Drysdale Dal Piaz, Giorgio Dal Piaz, Giorgio Dale, Henry Hallett Dale, Henry Hallett Dale, Henry Hallett Dall, William Healey Dalton, John Dalton, John Dalton, John Dalton, John Call Dalton, John Call Daly, Reginald Aldworth Daly, Reginald Aldworth Dam, Henrik Dam, Henrik Dana, James Dwight Dandelin, Germinal Pierre Dandelin, Germinal Pierre Danforth, Charles Haskell Danforth, Charles Haskell Daniell, John Frederic Daniell, John Frederic Daniell, John Frederic Daniels, Farrington Danti, Egnatio Danti, Egnatio Dantzig, David van Dantzig, David van Dantzig, David van Darboux, Jean-Gaston D'Arcet, Jean D'Arcy, Patrick D'Arcy, Patrick Darlington, Cyril Dean Darlington, William Darwin, Charles Galton Darwin, Charles Galton Darwin, Charles Robert Darwin, Charles Robert Darwin, Charles Robert Darwin, Erasmus Darwin, Erasmus Darwin, Erasmus Darwin, Erasmus Darwin, Francis Darwin, George Howard Darwin, George Howard Dasypodius, Cunradus Dasypodius, Cunradus Daubenton, Louis-Jean-Marie Daubenton, Louis-Jean-Marie

29. Technology/ Engineering Translate this page dandelin, germinal Pierre. Darwin, Erasmus. Davidov, August Yulevich. De Groot,Jan Cornets. De La Rue, Warren. Delaunay, Charles-Eugène. Deprez, Marcel http://www.indiana.edu/~newdsb/tech.html

Technology/ Engineering Agassiz, Alexander Alberti, Leone Battista Albrecht, Carl Theodor Amici, Giovan Battista Amsler, Jakob Archimedes Armstrong, Edwin Howard Ayrton, Hertha Babbage, Charles Baker, Henry Balbus Baldi, Bernardino Barkhausen, Heinrich Georg Bauer, Franz Andreas Beale, Lionel Smith Beckmann, Johann Beeckman, Isaac Bell, Alexander Graham Bellinsgauzen, Faddei F. Berger, Hans Berkner, Lloyd Viel Bernoulli, Jakob Bessemer, Henry Betancourt y Molina, Augustin de Bion, Nicolas Borelli, Giovanni Alfonso Borries, Bodo von Bossut, Charles Bour, Edmond Boussinesq, Joseph Valentin Brashman, Nikolai Dmitrievich Brinell, Johan August Brioschi, Francesco Brown, Ernest William Brunelleschi, Filippo Bunyakovsky, Viktor Yakovlevich Buono, Paolo del Bush, Vannevar Cailletet, Louis Paul Callendar, Hugh Longbourne Campani, Giuseppe Carnot, Lazare-Nicolas- Marguerite Castelli, Benedetto Castigliano, Alberto Cauchy, Augustin-Louis Chaplygin, Sergei Alekseevich Charcot, Jean-Baptiste Chardonnet, Louis-Marie- Hilaire Bernigaud Christofilos, Nicholas Constantine Clairaut, Alexis-Claude

30. Math Lessons - Germinal Pierre Dandelin Math Lessons germinal Pierre dandelin. germinal Pierre dandelin. germinalPierre dandelin (1794 - 1847) was a mathematician, soldier, and professor of http://www.mathdaily.com/lessons/Germinal_Pierre_Dandelin

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more ... Mining engineers Germinal Pierre Dandelin Germinal Pierre Dandelin ) 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 . He was wounded fighting under Napoleon . He worked for the Ministry of the Interior under Lazare Carnot . Later he became a citizen of the Netherlands , a professor of mining engineering in Belgium , and then a member of the Belgian army. He is the eponym of the Dandelin spheres , of Dandelin's theorem in geometry (for an account of that theorem, see Dandelin spheres stereographic projection algebra , and probability theory References Biography in Dictionary of Scientific Biography (New York 1970-1990). F Cajori, The Dandelin-Gräffe method , in A history of Mathematics (New York, 1938), 364.

31. Mathematics Animated Tracing a Parabola with Quetelet dandelin A proof of Quetelet dandelin the Belgian geometers Adolphe Quetelet and germinal dandelin devised a simple http://clem.mscd.edu/~talmanl/MathAnim.html

Mathematics Animated Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State College of Denver The objects below are QuickTime animations; they should work on Macintosh computers or on Windoze boxes that have QuickTime installed. If you don't have QuickTime, you can get the latest version at Apple's QuickTime site This page has proved to be much more popular than I could ever have imagined that it would, and I've heard complaints from several sources that it includes little or no explanation of what the animations illustrate. My original intent was that knowlegeable instructors would use the movies with their students; of course, such instructors would already know what was going on and would provide their own explanations. However, to my amazement and gratification, many more people other than instructors appear to have found something (or things) that they like hereso explanations may now be needed. Over the next few months, I will try to add some. Bill Emerson, Brad Kline, and I gave an MAA Minicourse in creating and exporting animations like these to the Web at the Joint Mathematics Meetings in New Orleans during January of 2001 and in San Diego during January of 2002. Bill and I also gave a workshop at the Spring 2002 meeting of the Rocky Mountain Section of the MAA in Laramie, WY, in April of 2002. We're always happy to discuss these techniques. Write.

32. KöMaL - Rita Kós: Conics And Dandelin Spheres germinal Pierre dandelin (17941847) was a French engineer, who lived in Belgium.In 1822, he discovered the relation between the intersection curve of the http://www.komal.hu/cikkek/dandelin/dandelin.e.shtml

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. If the angle is equal to the half of the apex angle of the cone, the intersection curve is a parabola ; if it is smaller than the half-angle, then the intersection is a hyperbola; if the angle is greater than the half-angle, then the curve is an ellipse ; and finally, if the plane is perpendicular to the axis, then the intersection is a circle The curves listed above can also be considered as the loci of points of certain properties. The parabola is the locus of those points in the plane that are equidistant from a fixed point, called the focus , and a fixed straight line, called the directrix. The ellipse is the locus of those points in the plane for which the sum of the distances from two given points - the so-called foci - is constant. The hyperbola is the locus of those points in the plane for which the difference between the distances from two given points - the so-called foci - is constant.

33. Biography-center - Letter D dandelin, germinal ww whistory.mcs.st-and.ac.uk/~history/Mathematicians/dandelin.html;Dandy, Walter Edward www.whonamedit.com/doctor.cfm/447.html http://www.biography-center.com/d.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish D 497 biographies D aly, Tyne www.cbs.com/primetime/judging_amy/bio_tdaly.shtml D anzi, Franz www.naxos.com/composer/danzi.htm D eforest, Lee web.mit.edu/invent/www/inventorsA-H/deforest.html D elluc, Louis www.lips.org/bio_delluc_GB.asp D epardieu, G©rard www.depardieu.8m.com/bio.html D ickens, Charles www.fidnet.com/~dap1955/dickens/ D ouglass, Frederick odur.let.rug.nl/~usa/B/fdouglas/dougxx.htm D rouais, Fran§ois-Hubert www.kfki.hu/~arthp/bio/d/drouais/biograph.html www-history.mcs.st-and.ac.uk/~history/Mathematicians/Durer.html D'Alema, Massimo www.uwgb.edu/galta/333/BIOS98/DALEMA.H TM d'Alembert, Jean-le-Rond www.treasure-troves.com/bios/dAlembert .html d'Alembert, Jean www-hi story.mcs.st-and.ac.uk/~history/Mathematicians/D'Alembert.html D'Inzeo, Raimondo

34. Dandelin They were so much of a mystery that 200 years after Kepler, in the 19th century,a Belgian geometer named germinal dandelin gave a remarkable geometric http://joma.org/images/upload_library/4/ellipses/footnotes/footnote1.htm

Note 1. The Dandelin Spheres While it is easy to prove these facts analytically given the standard form equation for a general ellipse, the proof never reveals why that they should be true. They were so much of a mystery that 200 years after Kepler , in the 19th century, a Belgian geometer named Germinal Dandelin gave a remarkable geometric proof of the focus-locus property of ellipses, using a construction that has come to be known as the Dandelin spheres The main picture of his construction is shown below, and you may learn more about his argument in Eric Weisstein's article at mathworld

35. Dandelin They were so much of a mystery that 200 years after Kepler in the 19th century,a Belgian Geometer named germinal dandelin gave a remarkable geometric proof http://www.mathwright.com/library6/footnote1.htm

While it is easy to prove these facts analytically given the standard form equation for a general ellipse, the proof never reveals why that they should be true. They were so much of a mystery that 200 years after Kepler in the 19th century, a Belgian Geometer named Germinal Dandelin gave a remarkable geometric proof of the focus-locus property of ellipses using a construction that has come to be known as the Dandelin spheres. The main picture of his construction is shown below, and you may learn more about his argument in Eric Weisstein's article at mathworld

36. Dandelin Translate this page dandelin, germinal Pierre, belgischer Mathematiker * 12. 4. 1794 Le Bourget, † 15.2. 1847 Ixelles. Arbeitsgebiete Kegelschnitte http://www.studienseminare-duesseldorf.nrw.de/sekundI/Seminare/Mathe/Kaleidoskop

Zurück zur Übersicht Biografien Dandelin , Germinal Pierre, belgischer Mathematiker Arbeitsgebiete: Kegelschnitte Nach Dandelin sind die Dandelinschen Kugeln benannt: eine bzw. zwei Kugeln, die sämtlich Mantellinien eines geraden Kreiskegels und eine Schnittebene in den Brennpunkten des entstehenden Kegelschnitts berühren; die Dandelinschen Kugeln dienen der Herleitung der Eigenschaften von Kegelschnitten.

37. Xah: Special Plane Curves: Conic Sections dandelin sphere relate many properties of the conics to the cone. It is namedafter its discoverer germinal Pierre dandelin (1822). http://www.xahlee.org/SpecialPlaneCurves_dir/ConicSections_dir/conicSections.htm

If you spend more than 30 minutes on this site, please send $1 to me. Go to http://paypal.com/ and make a payment to xah@xahlee.org. Or send to: P. O. Box 390595, Mountain View, CA 94042-0290, USA. ☠Back to Table of Contents Conic Sections Intersections of parallel planes and a double cone, forming ellipses parabolas , and hyperbolas respectively. graphics code cone_cut.gcf Mathematica Notebook for This Page History ... Related Web Sites History Appollonius was the first to base the theory of all three conics on sections of one circular cone, right or oblique. He is also the one to give the name ellipse, parabola, and hyperbola. A brief explanation of the naming can be found in Howard Eves, An Introduction to the History of Math. 6th ed. page 172. (also see J.H.Conway's newsgroup message, link at the bottom) In Renaissance, Kepler's law of planetary motion, Descarte and Fermat's coordinate geometry, and the beginning of projective geometry started by Desargues, La Hire, Pascal pushed conics to a high level. 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. Among the contributors, we may find Newton, Dandelin, Gergonne, Poncelet, Brianchon, Dupin, Chasles, and Steiner. Conic sections is a rich classic topic that has spurred many developments in the history of mathematics. Description Hyperbola ellipse , and parabola are together known as conic sections, or just conics. So called because they are the intersection of a right circular cone and a plane.

38. Glace En Cône Pour ceux quidésirent connaître mieux dandelin, germinal Pierre dandelin est né au Bourget http://hypo.ge-dip.etat-ge.ch/www/math/html/node86.html

Sommaire Escher et math L'exercice s'inspire du livre Mathematic in Action de Stan Wagon, Springer, New York, 1999 et de divers sites Internet. Indications et et la pente m et et , le point d'intersection M M aux centres et et Pour calculer On obtient alors: z en fonction de y M et M M P et Q . Les segments MA et MP M . Les segments MB et MQ Comme la longueur du segment PQ est constante quelque soit le point M (puisque P et Q A et B sont tels que pout tout point M de l'ellipse: Donc les points A et B sont bien les foyers de l'ellipse. Solutions dandelin.m Sommaire Escher et math Jean-Bernard ROUX Jean-Bernard Roux

39. Acquiring Statistics | Adolphe Quetelet turned out acceptable paintings of his own, wrote poetry, and with his friendand fellow FrancoBelgian germinal dandelin, collaborated on an opera. http://www.umass.edu/wsp/statistics/tales/quetelet.html

Tales of Statisticians Adolphe Quetelet 22 Feb 1796 - 17 Feb 1874 Quetelet was born in Ghent, to a French father who had established himself there ten years earlier, and a Brabantine mother. The son successfully negotiated the upheavals which were being caused by the 1790 transition from the Austrian to the French Republican educational structures in the Austrian Netherlands, showing in the process a talent for the uses to which new institutions can be put. This skill was to serve him well in later life. In 1823 Brussels became again part of the southern Netherlands. Quetelet made contact with the Minister of Public Education, and interested him in the founding of an observatory in Brussels. Quetelet was sent to Paris to learn the requisite techniques. Among the things he learned, from contacts with Laplace, Fourier, and Poisson, was the central importance of probability theory in astronomy. Back in Brussels, Quetelet gave popular lectures at the Brussels Museum on probability as well as astronomy and physics; he added to his knowledge (and his collection of scientific instruments) by visiting other centers; he founded a journal. In 1826, being increasingly interested in the social aspect of his probability studies, he published a paper on the laws of births and mortality in Brussels, and subsequently advocated a complete population census, which was ordered by the government in 1828. In that year, Quetelet was appointed astronomer of the Brussels Observatory (which at that time was still 4 years short of completion).

40. Gale-Edit - Dictionary Of Science Biography - Scientists By Name Reginald Aldworth; Dam, Henrik; Dana, James Dwight; dandelin, germinal Pierre;Danforth, Charles Haskell; Daniell, John Frederic; Daniels, Farrington http://www.gale-edit.com/ndsb/scientists.htm

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