The Double Bubble Conjecture « OU Math Club Jan 26, 2010 This is the Double Bubble Conjecture. In 1995 it was proven by Hass, Hutchings, and Schlafy in the special case that both bubbles have the http://oumathclub.wordpress.com/2010/01/26/the-double-bubble-conjecture/
Historia Matematica Mailing List Archive: [HM] Double Bubble Co Research Announcement, February 25, 2000 Proof of the Double Bubble Conjecture by Michael Hutchings, Frank Morgan, Manuel Ritore, and Antonio Ros http://sunsite.utk.edu/math_archives/.http/hypermail/historia/mar00/0093.html
Proof Of The Double Bubble Conjecture In Rn Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.springerlink.com/index/M42036623635477V.pdf
Proof Of The Double Bubble Conjecture In R4 And Certain Higher PACIFIC JOURNAL OF MATHEMATICS Vol. 208, No. 2,2003 PROOF OF THE DOUBLE BUBBLE CONJECTURE INR 4 AND CERTAIN HIGHER DIMENSIONAL CASES BenW. Reichardt, Cory Heilmann, Yuan Y. Lai, and http://pjm.math.berkeley.edu/pjm/2003/208-2/pjm-v208-n2-p09-p.pdf
Proof Of The Double Bubble Curvature Conjecture Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.springerlink.com/index/A1160637U5876501.pdf
Double Bubble Conjecture [Archive] - Physics Forums Archive Double Bubble Conjecture General Math Well, you can start off with Mathworld (http//mathworld.wolfram.com/DoubleBubble.html). http://www.physicsforums.com/archive/index.php/t-1086.html
Electronic Research Announcements The double bubble conjecture Author(s) Joel Hass; Michael Hutchings; Roger Schlafly http://www.ams.org/era/1995-01-03/S1079-6762-95-03001-0/home.html
Proof Of The Double Bubble Conjecture Outdated Archival Version. These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://www.kurims.kyoto-u.ac.jp/EMIS/journals/ERA-AMS/2000-01-006/2000-01-006.ht
Extractions: These pages are not updated anymore. They reflect the state of 20 August 2005 . For the current production of this journal, please refer to http://www.math.psu.edu/era/ This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/ Abstract. Retrieve entire article TeX source
THE DOUBLE BUBBLE CONJECTURE File Format Adobe PostScript View as HTML http://emis.impa.br/EMIS/journals/ERA-AMS/1995-03-001/1995-03-001.ps
Double Bubble Conjecture Two partial Spheres with a separating boundary (which is planar for equal volumes) separate two volumes of air with less Area than any other boundary. http://mathserver.sdu.edu.cn/mathency/math/d/d385.htm
Extractions: Two partial Spheres with a separating boundary (which is planar for equal volumes) separate two volumes of air with less Area than any other boundary. The planar case was proved true for equal volumes by J. Hass and R. Schlafy in 1995 by reducing the problem to a set of 200,260 integrals which they carried out on an ordinary PC. See also Double Bubble
Nsf.gov - National Science Foundation (NSF) Discoveries - Double The team's solution of the Double Bubble Conjecture was announced in March 2000 before the Undergraduate Mathematics Conference at the RoseHulman Institute of Technology, and has http://www.nsf.gov/discoveries/disc_summ.jsp?cntn_id=100596&org=NSF
Mathematical Recreations A notorious case is the Double Bubble Conjecture, which states that the shape formed when two bubbles coalesce consists of three spherical surfaces. http://www.fortunecity.com/emachines/e11/86/bubble.html
Extractions: Web hosting Custom Email SiteBuilder Mathematical Recreations by Ian Stewart The dodecahedron has 20 vertices, 30 edges and 12 faces- each with five sides. But what solid has 22.9 vertices, 34.14 edges and 13.39 faces -each with 5.103 sides? Some kind of elaborate fractal , perhaps? No, this solid is an ordinary, familiar shape, one that you can probably find in your own home. Look out for it when you drink a glass of cola or beer, take a shower or wash the dishes. I've cheated, of course. My bizarre solid can be found in the typical home in much the same manner that, say, 2.3 children can be found in the typical family. It exists only as an average. And it's not a solid; it's a bubble. Foam contains thousands of bubbles, crowded together like tiny, irregular polyhedra-and the average number of vertices, edges and faces in these polyhedra is 22.9, 34.14 and 13.39, respectively. If the average bubble did exist, it would be like a dodecahedron , only slightly more so.
Computer Images Of Double Bubbles By John Sullivan I created these images to illustrate the proof of the equalvolume case of the Double Bubble Conjecture by Hass and Schlafly in 1995. The bottom row shows a standard double bubble http://torus.math.uiuc.edu/jms/Images/double/
Extractions: These images show bubble clusters near equilibrium. The top row shows a standard double bubble of equal volumes, and a nonstandard cluster in which one bubble is a torus, forming a waist around the other. I created these images to illustrate the proof of the equal-volume case of the Double Bubble Conjecture by Hass and Schlafly in 1995. The bottom row shows a standard double bubble of unequal volumes (consisting of three spherical caps meeting at equal 120-degree angles), and a nonstandard bubble of the same volumes, in which the larger region is broken into two components (one a tiny ring around the other region). I created these images to illustrate the proof of the general Double Bubble Conjecture by Hutchings, Morgan, Ritore and Ros in 2000. In all four cases, the cluster is a surface of revolution. More details about the geometry of the examples with unequal volumes, including pictures of the generating curves, are available
The Double Bubble Conjecture Outdated Archival Version. These pages are not updated anymore. They reflect the state of 20 August 2005. For the current production of this journal, please refer to http://emis.library.cornell.edu/journals/ERA-AMS/1995-03-001/1995-03-001.html
Extractions: These pages are not updated anymore. They reflect the state of 20 August 2005 . For the current production of this journal, please refer to http://www.math.psu.edu/era/ This journal is archived by the American Mathematical Society. The master copy is available at http://www.ams.org/era/ Comments on article Abstract. Retrieve entire article TeX source PostScript Joel Hass Department of Mathematics, University of California, Davis, CA 95616 E-mail address: hass@math.ucdavis.edu Michael Hutchings Department of Mathematics, Harvard University, Cambridge, MA 02138 E-mail address: hutching@math.harvard.edu Roger Schlafly Real Software, PO Box 1680, Soquel, CA 95073
