Double Bubble Conjecture - Technology Services View Thread double bubble conjecture. Click Here double bubble conjecture. loopquantum gravity. what is it and how was it prooved? Enter Physics Chat. http://www.physicsforums.com/archive/t-1086
Extractions: Physics Help and Math Help - Physics Forums Mathematics General Math Archives View Thread : Double Bubble Conjecture loop quantum gravity what is it and how was it prooved? Zefram Well, you can start off with Mathworld (http://mathworld.wolfram.com/DoubleBubble.html). Real Estate Exchange Import Auto N' Car Parts Oakley Replica ... Car Body Parts
Electronic Research Announcements Math DigestAmerican Mathematical Society News Release. A Mathematical Milestone DoubleBubble Conjecture Proved. double bubble conjecture World Wide Web sources http://www.ams.org/journal-getitem?pii=S1079-6762-00-00079-2
Mathenomicon.net : News : Double Bubbles A proof of the double bubble conjecture has been announced at theRoseHulman Institute of Technology in Indiana, United States. http://www.cenius.net/news/news.php?ArticleID=0
Mathenomicon.net : News : Archive 21th March 2000 Double bubbles A proof of the double bubble conjecture has been announcedat the RoseHulman Institute of Technology in Indiana, United States. http://www.cenius.net/news/archive/default.php
Double Bubble Minimizes: Applications To Geometry J. Hass, M. Hutchings, and R. Schlafly, The double bubble conjecture, ElectronicResearch Announcements of the American Mathe. Society, 1995, Vol. 1, pp. http://www.cs.utep.edu/interval-comp/bubble.html
Extractions: It is well known that of all surfaces surrounding an area with a given volume V, the sphere has the smallest area. This result explains, e.g., why a soap bubble tends to become a sphere. More than a hundred years ago, the Belgian physicist J. Plateaux asked a similar question: what is the least area surface enclosing two equal volumes? Physical experiments with bubbles seem to indicate that the desired least area surface is a "double bubble", a surface formed by two spheres (separated by a flat disk) that meet along a circle at an angle of 120 degrees. However, until 1995, it was not clear whether this is really the desired least area surface. Several other surfaces ("torus bubbles") have been proposed whose areas are pretty close to the area of the double bubble. The theorem that double bubble really minimizes was recently proven by Joel Hass from Department of Mathematics, University of California at Davis (email hass@math.ucdavis.edu
Historia Matematica Mailing List Archive: [HM] Double Bubble Co HM double bubble conjecture Proved. Proof of the double bubble conjecture. by MichaelHutchings, Frank Morgan, Manuel Ritore, and Antonio Ros. quote History. http://sunsite.utk.edu/math_archives/.http/hypermail/historia/mar00/0093.html
Cwikel Frank Morgan Williams College. Proof of the double bubble conjecture.Abstract. The double bubble conjecture says that the familiar http://www.math.princeton.edu/~seminar/2002-03-sem/MorganAbstract10-7-2002.html
Seminar Week of October 7 October 11, 2002. Analysis Seminar. Topic Proof ofthe double bubble conjecture. Presenter Frank Morgan, Williams College. http://www.math.princeton.edu/~seminar/2002-03-sem/9-26-2002weekly.html
Extractions: PACM Colloquium Topic: The Level Set Method and Schroedinger's Equation Presenter: Li-Tien Cheng , University of California, San Diego Date: Monday, September 30, 2002, Time: 4:00 p.m., Location: Fine Hall 214 Abstract: The level set method has recently been succesfully applied to the construction wavefronts in geometrical optics. We extend the approach here to wavefronts found in Schroedinger's equation as well as other quantities of interest. Advantages such as an Eulerian foundation and the ability to handle multivaluedness are preserved in the extension.
Mathematical Recreations A notorious case is the double bubble conjecture, which states that the shapeformed when two bubbles coalesce consists of three spherical surfaces. http://www.fortunecity.com/emachines/e11/86/bubble.html
Extractions: web hosting domain names email addresses 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.
Double Bubble Conjecture double bubble conjecture. Haas, J.; Hutchings, M.; and Schlafy, R. ``The Double BubbleConjecture. Electron. Res. Announc. Amer. Math. Soc. 1, 98102, 1995. http://icl.pku.edu.cn/yujs/MathWorld/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
Double Bubble See also Apple, Bubble, double bubble conjecture, SphereSphere Intersection.References. Morgan, F. ``The double bubble conjecture. FOCUS 15, 6-7, 1995. http://icl.pku.edu.cn/yujs/MathWorld/math/d/d384.htm
Extractions: References Campbell, P. J. (Ed.). Reviews. Math. Mag. Foisy, J.; Alfaro, M.; Brock, J.; Hodges, N.; and Zimba, J. ``The Standard Double Soap Bubble in Uniquely Minimizes Perimeter.'' Pacific J. Math. Morgan, F. ``The Double Bubble Conjecture.'' FOCUS Peterson, I. ``Toil and Trouble over Double Bubbles.'' Sci. News , 101, Aug. 12, 1995.
Lecture 5 Frank Morgan will give nine lectures on the subject of Geometric MeasureTheory and the Proof of the double bubble conjecture. Last http://zeta.msri.org/calendar/talks/TalkInfo/511/show_talk
Extractions: Last year Hutchings, Morgan, Ritore and Ros announced a proof of the Double Bubble Conjecture, which says that the familiar standard double soap bubble provides the least-area way to enclose and separate two given volumes of air. It was only with the advent of geometric measure theory in the 1960s that mathematicians were ready to deal with such problems involving surfaces meeting along singularities in unpredictable ways. The lectures will discuss modern, measure-theoretic definitions of "surface," compactness of spaces of surfaces, and finally the proof of the double bubble conjecture. Homework will vary from basic exercises to open problems. The text Geometric Measure Theory: A Beginner's Guide (3rd edition) by Frank Morgan will be made available, as well as additional notes and materials. (Students nominated by MSRI sponsors will receive a copy of the book on arrival. Several copies will be available for use by other participants.) There will be sessions on exercises and on open problems.
Michigan Undergraduate Mathematics Conference 2002 Double Bubble No More Trouble in November 2000 Math Horizons; Proof of thedouble bubble conjecture in March 2001 American Mathematical Monthly. http://www.calvin.edu/academic/math/mumc2002/
Extractions: [Featured Speaker] [Keynote Address] [Student Talks] [Poster] ... Who Wants to Be a Mathematician? The 2003 MUMC will be held at the University of MichiganDearborn on Saturday, February 15, 2003. Visit the conference website for additional information. There are a number of other Undergraduate Mathematics Conferences across the country. Here are links to a few of them: Frank Morgan from Williams College will be our feature speaker. Frank Morgan is currently the Second Vice-President of the Mathematical Association of America and has long been involved in undergraduate research projects and has advised numerous students and groups of students at both graduate and undergraduate levels. At Williams College, where he currently teaches in the Mathematics and Statistics Department, he was the founding director of the very successful SMALL undergraduate research project Professor Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various dimensions and settings. (If you don't know what that means, think of soap bubbles as 2-dimensional surfaces in a 3-dimensional space.) He has written four books:
BBC News | SCI/TECH | Double Bubble Is No Trouble Four mathematicians have announced a proof of the socalled double bubble conjecture- that the familiar double soap bubble is the optimal shape for enclosing http://news.bbc.co.uk/hi/english/sci/tech/newsid_685000/685243.stm
Extractions: By BBC News Online science editor Dr David Whitehouse Four mathematicians have announced a proof of the so-called Double Bubble Conjecture - that the familiar double soap bubble is the optimal shape for enclosing and separating two chambers of air. In an address to the Undergraduate Mathematics Conference at the Rose-Hulman Institute of Technology in Indiana, Frank Morgan of Williams College, Massachusetts, announced that he, Michael Hutchings of Stanford, and Manuel Ritori and Antonio Ros of Granada, had finally proved what the double soap bubble had known all along. When two round soap bubbles come together, they form a double bubble. Unless the two bubbles are the same size, the surface between them bows a bit into the larger bubble. The separating surface meets each of the two bubbles at 120 degrees. Mathematicians have expressed surprise that when two bubbles are joined in this way that the interior surface that separates them is not bowed all that much.
Extractions: Vol. 151, No. 2, pp. 459-515 (2000) Previous Article Next Article Contents of this Issue Other Issues ... EMIS Home Review from Zentralblatt MATH Zbl 0970.53009 )], see the review below. Reviewed by Robert Finn Keywords: double bubble conjecture; equal volumes; spherical cap Classification (MSC2000): Full text of the article: Electronic fulltext finalized on: 27 Apr 2001. This page was last modified: 22 Jan 2002. Johns Hopkins University Press
Search Results An = (0970.53008) ISSN 0003486X The authors prove the ``double bubble conjecture in$\bbfR^3$, in the particular case in which the two volumes are equal. http://www.emis.de/MATH-item?0970.53008
University Of Pittsburgh: Department Of Mathematics The problem of two bubbles, known as the double bubble conjecture, was solvedonly recently by J. Hass, M. Hutchings, and R. Schlafy.(The double bubble http://www.math.pitt.edu/articles/kelvin.html
Extractions: If we turn to the next page after the Kepler conjecture in Kepler's Six-Cornered Snowflake , we find a discussion of the structure of the bee's honeycomb. The rhombic dodecahedron was discovered by Kepler through close observation of the honeycomb. The honeycomb is a six-sided prism sealed at one end by three rhombi. By sealing the other end with three additional rhombi, the honeycomb cell is transformed into the rhombic dodecahedron. Figure 8 The cannonball packing of balls leads to honeycomb cells. It is also related to more general foam problems. If we tile space with hollow rhombic dodecahedra, and imagine that each has walls made of a flexible soap film, we have an example of a foam. The problem of foams, first raised by Lord Kelvin, is easy to state and hard to solve. How can space be divided into cavities of equal volume so as to minimize the surface area of the boundary? The rhombic dodecahedral example is far from optimal. Lord Kelvin proposed the following solution. Truncated octahedra fill space (see Figure 9).
MAA: Math Horizons--Subscribe On March 18, 2000 an international team of mathematicians announced a proof of thedouble bubble conjecture, which says that the familiar double soap bubble http://faculty.oxy.edu/jquinn/Math_Horizons/teasers/teasers11-00.html
Extractions: Ideas? Content Teasers for November 2000 On March 18, 2000 an international team of mathematicians announced a proof of the Double Bubble Conjecture, which says that the familiar double soap bubble provides the least-area way to enclose and separate two given volumes of air. The two spherical caps are separated by a third spherical cap, all meeting at 120-degree angles. (If the volumes are equal, the separating surface is a flat disc.) This result is the culmination of ten years of remarkable progress by a number of mathematicians including several undergraduate students. The first step was the realization that the problem is actually quite difficult. Be honest. There have been times when you voted strategically to try to force a personally better election result; I have. The role of manipulative behavior received brief attention during the 2000 US Presidential Primary Season when the Governor of Michigan failed on his promise to deliver his state's Republican primary vote for George Bush. His excuse was that the winner, John McCain, strategically attracted cross-over votes of independents and Democrats. When I was about 10 I remember getting a puzzle in my stocking which consisted of a 4 x 4 grid with 15 square pieces in it. Of course, there was one space in the grid that held no piece, and you could slide the pieces around so that a piece next to the "hole" could be slid into that space. This particular puzzle had the pictures of four comic book figures when solved. However, you could move the pieces around to give some of the figures different heads, which added a great deal of fun for me. The box the puzzle came in gave some "impossible" positions, and I recall that at the time I wondered how they knew this. Today I still look for puzzles like these whenever I visit a toy store. Now, though, I find that the mathematics behind the puzzles intrigues me as much as the challenge of solving them.
MAA-NJ Spring 2001 Meeting President of the Mathematical Association of America, is part of the internationalteam of mathematicians who recently proved the double bubble conjecture. http://orion.ramapo.edu/~ldant/old/rowan01/programs01.html
Extractions: The Mathematical Association of America New Jersey Section - Spring Meeting Rowan University,Glassboro, NJ Saturday,April 21, 2001 Main Lecture Hall - Bosshart 203 Registration and Coffee - Second floor Lobby Bosshart Hall Book Exhibits Welcome byRonald Czochor, Chairperson, Department of Mathematics, Rowan University Graph Products and Cannon Pairs Joseph Loeffler, The College of New Jersey Student Speaker Presider: Cathy Liebars, The College of New Jersey Effective 3-D Visualizations of High Level Mathematical Functions Bonita Saunders, National Institute of Standards and Technology Presider: Bonnie Gold, Monmouth University Remarks by Chair of MAA-NJ Judith Lenk, Ocean County College Intermission (Coffee and Book Exhibits) Concurrent Sessions Workshop on Active Learning , by Janet Caldwell, Rowan University Campbell Library Commons Room 126 MAA-NJ Contributed papers I Bosshart 118 MAA-NJ Contributed papers - II Bosshart 116 MAA-NJ Contributed papers - III Bosshart 129 MAA-NJ Contributed papers - IV Bosshart 236 Student Contributed papers - Bosshart 316 Lunch (Book Exhibits end at 1:30) and Discussion Tables Student Center Ballroom Mathematics as Empirical Science Doron Zeilberger, Temple University
Student Papers At The NES/MAA Spring 2000 Meeting Session I double bubble conjectures Andrew Cotton, Harvard University and WilliamsCollege The double bubble conjecture in R 3 has recently been proved. http://www.southernct.edu/organizations/nesmaa/studentpapersspring2000.html
