Proof Of The Double Bubble Conjecture Jul 17, 2000 We prove that the standard double bubble provides the leastarea way to enclose and separate two regions of prescribed volume in ${\mathbb http://www.mpim-bonn.mpg.de/era-mirror/2000-01-006/2000-01-006.html
Extractions: PostScript Michael Hutchings Department of Mathematics, Stanford University, Stanford, CA 94305 E-mail address: hutching@math.stanford.edu Frank Morgan Department of Mathematics, Williams College, Williamstown, MA 01267 E-mail address: Frank.Morgan@williams.edu Manuel Ritoré Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, España E-mail address: ritore@ugr.es Antonio Ros Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, España
Furman Mathematics: Clanton Visiting Mathematician O n March 1, 2010, the Department of Mathematics hosted the 200910 Donald H. Clanton Visiting Mathematician Professor Donald G. Saari http://math.furman.edu/activities/clanton/
Extractions: Mathematically, a torus can be represented by the surface of a donut. While it may sound tasty, it is not clear of what value, or even interest, a torus can be. As shown in this lecture, expect it to explain all sorts of mysteries ranging from problems of vision, capturing emotions, the reason there are 435 representatives in the US Congress, and, should time permit, all sorts of other applications.
Nsf.gov - National Science Foundation (NSF) Discoveries - Double Oct 17, 2007 Ultimately, the proof of the Double Bubble Conjecture was gained by the team s use of The Double Bubble Conjecture is an example of what http://www.nsf.gov/discoveries/disc_summ.jsp?cntn_id=100596
Math Forum Discussions - Historia-Matematica Views expressed in these public forums are not endorsed by Drexel University or The Math Forum. http://mathforum.org/kb/forum.jspa?forumID=149
Frank Morgan (mathematician) - Wikipedia, The Free Encyclopedia He is most famous for proving the double bubble conjecture, that the minimumsurface-area enclosure of two given volumes is formed by three spherical patches meeting at 120-degree http://en.wikipedia.org/wiki/Frank_Morgan_(mathematician)
Extractions: Princeton University , 250-Anniversary Visiting Professorship for Distinguished Teaching (1997-98) Frank Morgan is an American mathematician and the Webster Atwell '21 Professor of Mathematics at Williams College , specialising in geometric measure theory and minimal surfaces Double bubble He is most famous for proving the double bubble conjecture , that the minimum-surface-area enclosure of two given volumes is formed by three spherical patches meeting at 120-degree angles at a common circle. Morgan is a vice-president-elect of the American Mathematical Society Morgan studied at the Massachusetts Institute of Technology and Princeton University , and received his Ph.D. from Princeton in 1977, under the supervision of
Double Bubble - Free Online EBook Collection PROOF OF THE DOUBLE BUBBLE CONJECTURE INR4 AND CERTAIN HIGHER DIMENSIONAL CASES Proof of the Double Bubble Conjecture in R http://www.pdftop.com/ebook/double bubble/
As últimas Do Mundo Da Matemática Here we announce a proof HMRR of the general Double Bubble Conjecture in R3, using stability arguments. See also Frank Morgan Double Bubble Conjecture Proved http://www.mat.uc.pt/~jaimecs/ult/ult.html
Extractions: Paul Erdos morreu dia 20/9/96 -1 is now the Largest Known Prime December 6, 2001 > Michael Cameron, a 20 year-old volunteer in a worldwide research project called the Great Internet Mersenne Prime Search (GIMPS) , has discovered the largest known prime number using his PC and software by George Woltman and Entropia, Inc.
The Double Bubble Conjecture by J Hass Cited by 49 - Related articles http://www.emis.de/journals/ERA-AMS/1995-03-001/1995-03-001.html.old
Ivars Peterson's MathTrek -Prized Geometric Logic Last summer, Andrew Cotton and David Freeman proved the double bubble conjecture for equal volumes in hyperbolic and spherical space. Despite such progress, many questions about http://www.maa.org/mathland/mathtrek_6_18_01.html
Extractions: Ivars Peterson's MathTrek June 18, 2001 Predicting the geometric shapes of soap bubble clusters can lead to surprisingly difficult mathematical problems. Frank Morgan of Williams College in Williamstown, Mass., recently illustrated such difficulties when he invited an audience of mathematicians, students, and others to vote on which one of a given pair of different representations of the same number of clustered planar bubbles would have a smaller total perimeter. Assembled for a ceremony at the National Academy of Sciences in Washington, D.C., to honor the 12 winners of the 2001 U.S.A. Mathematical Olympiad (USAMO), audience members were wrong as often as they were right. Which one of these two configurations of five planar bubbles of equal area has the smaller total perimeter? The more symmetric candidate isn't always the winner. Courtesy of Frank Morgan. Even the case when two bubbles join to form a double bubblea sight familiar to any soap-bubble aficionadohas posed problems for mathematicians. In this case, the two bubbles share a disk-shaped wall, and this divider meets the individual bubbles' walls at an angle of 120 degrees. Mathematicians call this configuration the standard double bubble. If the bubbles are of equal size, the interface is flat. If one bubble is larger than the other, the rounded surface of the boundary film bulges into the bigger bubble. http://www.math.uiuc.edu/~jms/Images/double/
Science Blog -- Double Bubble Conjecture Proven WILLIAMSTOWN, Mass., March 28, 2000 Four mathematicians have announced a mathematical proof of the Double Bubble Conjecture that the familiar double http://scienceblog.com/community/older/2000/F/200005376.html
Furman Mathematics: Morgan Abstracts Abstracts for Frank Morgan, Clanton Visiting Mathematician, 20022003. PROOF OF THE DOUBLE BUBBLE CONJECTURE http://math.furman.edu/activities/clanton/morgan.html
Extractions: PROOF OF THE DOUBLE BUBBLE CONJECTURE ABSTRACT: A single round soap bubble provides the most efficient, least-area way to enclose a given volume of air. The Double Bubble Conjecture says that the familiar double soap bubble which forms when two soap bubbles come together provides the most efficient way to enclose and separate two given volumes of air. We'll discuss the problem, the recent proof, important contributions by undergraduates, and remaining open problems.
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
Bubbles And Math Olympiads - Science News Jan 14, 2010 The year 2000 finally saw a proof of the doublebubble conjecture for the case where the two volumes are unequal. http://www.sciencenews.org/view/generic/id/1741/title/Math_Trek__Bubbles_and_Mat
Extractions: Home Columns Math Trek Column entry Bubbles and Math Olympiads By Ivars Peterson Web edition Text Size Enlarge Which one of these two configurations of five planar bubbles of equal area has the smaller total perimeter? The more symmetric candidate isn't always the winner. Frank Morgan Predicting the geometric shapes of soap bubble clusters can lead to surprisingly difficult mathematical problems. Frank Morgan of Williams College in Williamstown, Mass., recently illustrated such difficulties when he invited an audience of mathematicians, students, and others to vote on which one of a given pair of different representations of the same number of clustered planar bubbles would have a smaller total perimeter. Assembled for a ceremony at the National Academy of Sciences in Washington, D.C., to honor the 12 winners of the 2001 U.S.A. Mathematical Olympiad (USAMO), audience members were wrong as often as they were right. "These are very tricky questions," Morgan says. "You often can't even come up with reasonable conjectures."
Extractions: Preprint Report number arXiv:0705.1601 Title Proof of the Double Bubble Conjecture in R^n Author(s) Reichardt, Ben W Imprint 23 May 2007. - 20 p. Note Comments: 20 pages, 22 figures Subject category Mathematical Physics and Mathematics Abstract The least-area hypersurface enclosing and separating two given volumes in R^n is the standard double bubble. Record created 2007-06-08, last modified 2008-12-16 Similar records
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