41. Furman Mathematics: Morgan Abstracts PROOF OF THE double bubble conjecture. ABSTRACT A single round soap bubble providesthe most efficient, leastarea way to enclose a given volume of air. http://math.furman.edu/activities/clanton/morgan.html

Furman Mathematics Department People Resources Activities ... Advice Abstracts for Frank Morgan, Clanton Visiting Mathematician, 2002-2003 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. THE SOAP BUBBLE GEOMETRY CONTEST ABSTRACT: A guessing contest with demonstrations, explanations, prizes, and some recent math news, including new results by undergraduates.

42. Stcon00 The double bubble conjecture says that the familiar double soap bubble providesthe leastarea way to enclose and separate two given volumes of air. http://home.moravian.edu/public/math/ClubsEvents/Conference/Archives/stcon00.htm

MORAVIAN COLLEGE STUDENT MATHEMATICS CONFERENCE Saturday, February 26, 2000 The conference is sponsored by the Moravian College chapter of Pi Mu Epsilon, with support from USG and Lehigh Valley Association of Independent Colleges (LVAIC): Allentown College Lehigh University Cedar Crest College Moravian College Lafayette College Muhlenberg College Additional Information Fees, tentative schedule, directions and deadlines. Call For Papers Presentation details. Link to last year's conference Link to 2001's conference Collier Hall of Science Moravian College Bethlehem, PA Invited Address: "Bursting the Double Bubble" By Frank Morgan Professor of Mathematics Williams College Computer graphics image by John M. Sullivan , University of Illinois, Urbana Champaign. For more information about Double Bubbles, please click here Abstract: A single round soap bubble provides the least-area way to enclose a given volume of air. The Double Bubble Conjecture says that the familiar double soap bubble provides the least-area way to enclose and separate two given volumes of air. Much media attention focussed on the recent proof using computers for the case of equal volumes, which in turn can be traced to undergraduate research. Now there are rumors from Spain of a proof for arbitrary volumes in R3, and an extension to R4 by undergraduates. Call For Papers The Moravian College chapter of Pi Mu Epsilon invites you to the fourteenth annual MORAVIAN COLLEGE STUDENT MATHEMATICS CONFERENCE on February 26, 2000, a unique opportunity for undergraduate students in the Tri-State area to meet and discuss mathematics. The day begins with a lively

43. Bubbles Science World, Bubble movie. Bubble Mania, Circumference/diameterwith bubbles. double bubble conjecture, Pictures of double bubbles. http://math.youngzones.org/bubbles.html

Bubbles, Bubbles Everywhere Everyone has fun blowing bubbles. But did you know that bubbles are mathematical? Bubble geometry Geometrical bubbles on wire frames Bubble prints Preserve your bubbles as art Antibubbles The opposite of a bubble Soap bubbles Create geometric art with soap films Zometool bubbles All about bubbles Exploratorium All about bubbles Activites for exploring bubbles Bubblesmith's gallery Bubble pictures WOW! Science World Bubble movie Bubble Mania Circumference/diameter with bubbles Double bubble conjecture Pictures of double bubbles

44. Go To Http//www.cs.appstate.edu/~sjg/class/1010/mathematician General double bubble conjecture in R^3 Solved, Focus The Newsletter of the MathematicalAssociation of America, May/June 2000, Volume 20, Number 5, p. 45. http://www.mathsci.appstate.edu/~sjg/class/1010/mathematician/mathematicianrefer

Go to http://www.cs.appstate.edu/~sjg/class/1010/mathematician/mathematicianreferences.html in order to click on the underlined web links. Note that if you see a reference to the Heart of Math book, then you should look there. Thomas Fuller One of Fuller's Calculations A History of Computers the history of computer speed MAD page http://www.math.buffalo.edu/mad/special/fuller_thomas_1710-1790.html African Slave and Calculating Prodigy: Bicentenary of the Death of Thomas Fuller, by Fauvel and Gerdes, Historia Mathematics 17 (1990), 141-151. The Great Mental Calculators: The Psychology, Methods, and Lives of Calculating Prodigies, Past and Present, by Steven B. Smith, 1983, On Mathematics in the History of Sub-Saharan Africa, by Paulus Gerdes, Historia Mathematica 21 (1994), 345-376, p. 345, 361-2, 366, 373. Maria Agnesi Maria Gaetana Agnesi The Living Witch of Agnesi http://www.astr.ua.edu/4000ws/witch-of-agnesi.html Why bother to learn Calculus - http://www.karlscalculus.org/why.html Definition of Calculus Women of mathematics : a biobibliographic sourcebook edited by Louise S. Grinstein p. 1-5. The Witch of Agnesi: A Lasting Contribution from the First Surviving Mathematical Work Written by a Woman - A commemoritive on the 200th anniversary of her death, by S. I. B. Gray and Tagui Malakyan, The College Mathematics Journal, Vol 30, No 4, September 1999, p. 258-268.

45. Tulane Math Colloquium: Fall 2003 Proof of the double bubble conjecture August 28 Frank Morgan, WilliamsCollege Abstract A single round soap bubble provides the http://www.math.tulane.edu/activities/colloquium/Fall_2003.html

Home Office hours Weekly activities Find people ... Summer research Lectures... Colloquium: Fall 2003 Go to... Lectures... Colloquium index Vigre seminars Undergrad seminar ... Clifford lectures Proof of the Double Bubble Conjecture August 28 Frank Morgan , Williams College Abstract A single round soap bubble provides the least-area way to enclose a given volume of air. The Double Bubble Conjecture says that the familiar double soap bubble provides the least-area way to enclose and separate two given volumes of air. I'll talk about the problem, the recent proof (Annals of Math. 2002), the latest results, and open questions. No prerequisites; undergraduates welcome. The Differential Geometry of Real-World Shapes: A Case Study - The Mylar Balloon and Elliptic Functions September 4 John Oprea , Cleveland State University Abstract When we look at Nature, we see shapes everywhere. But why do things take the shapes they do? In this talk, we will describe the shape of a Mylar balloon in terms of elliptic functions. (A Mylar balloon is often found at kids' birthday parties and is formed by taking two disks of Mylar, sewing them together along their boundaries and inflating.) This topic is a prime example of the interplay among physical principles, geometry, analysis and symbolic computation. Undergraduates are welcome.

46. Tulane Math Colloquium: Fall 2003 Fall 2003. Proof of the double bubble conjecture August 28 Frank Morgan,Williams College Abstract A single round soap bubble provides http://www.math.tulane.edu/activities/colloquium/2003-2004.html

Home Office hours Weekly activities Find people ... Summer research Lectures... Colloquium: 2003-2004 Go to... Lectures... Colloquium index Vigre seminars Undergrad seminar ... Clifford lectures Fall 2003 Proof of the Double Bubble Conjecture August 28 Frank Morgan , Williams College Abstract A single round soap bubble provides the least-area way to enclose a given volume of air. The Double Bubble Conjecture says that the familiar double soap bubble provides the least-area way to enclose and separate two given volumes of air. I'll talk about the problem, the recent proof (Annals of Math. 2002), the latest results, and open questions. No prerequisites; undergraduates welcome. The Differential Geometry of Real-World Shapes: A Case Study - The Mylar Balloon and Elliptic Functions September 4 John Oprea , Cleveland State University Abstract When we look at Nature, we see shapes everywhere. But why do things take the shapes they do? In this talk, we will describe the shape of a Mylar balloon in terms of elliptic functions. (A Mylar balloon is often found at kids' birthday parties and is formed by taking two disks of Mylar, sewing them together along their boundaries and inflating.) This topic is a prime example of the interplay among physical principles, geometry, analysis and symbolic computation. Undergraduates are welcome.

47. ScienceDaily -- Browse Topics: Science/Math/NumberTheory/DiophantineEquations/Fe Prove Double Soap Bubble Had It Right (March 20, 2000) — Four mathematicians haveannounced a mathematical proof of the double bubble conjecture that the http://www.sciencedaily.com/directory/Science/Math/NumberTheory/DiophantineEquat

Match: sort by: relevance date Free Services Subscribe by email RSS newsfeeds PDA-friendly format loc="/images/" A A A Find Jobs In: Healthcare Engineering Accounting College Contract / Freelance Customer Service Diversity Engineering Executive Healthcare Hospitality Human Resources Information Tech International Manufacturing Nonprofit Retail All Jobs by Job Type All Jobs by Industry Relocating? Visit: Moving Resources Moving Companies Mortgage Information Mortgage Calculator Real Estate Lookup Front Page Today's Digest Week in Review Email Updates ... Diophantine Equations Fermat's Last Theorem (22 links) News about Fermat's Last Theorem Magnetic Forces May Turn Some Nanotubes Into Metals (May 24, 2004) full story Streamlining The 'Pythagorean Theorem Of Baseball' (March 30, 2004) full story Cracking Data Hiding: Theory Can Help Disable Terrorists' Messages (July 15, 2003) full story Cutting The Noise Out Of Heartbeats (August 30, 2000) full story New Method Speeds Planning Of Space Missions (August 21, 2000) full story [ More news about Fermat's Last Theorem Books about Fermat's Last Theorem List Price: Amazon.com's Price:

48. Geometric Measure Theory, 3rd Edition Soap Bubble Clusters. Proof of double bubble conjecture. The HexagonalHoneycomb and Kelvin Conjectures. Immiscible Fluids and Crystals. http://www.harcourt-international.com/catalogue/title.cfm?ISBN=0125068514

49. Colloquium_abstracts The double bubble conjecture says that the familiar double soap bubble isthe leastarea way to enclose and separate two given volumes of air. http://www.wam.umd.edu/~jda/colloquium2_old.html

Abstracts of Colloquium talks Math Department UMD - College Park Other Seminars (February 2) Brian Marcus Coding Theory and Symbolic Dynamics In this talk we will describe several results and open problems regarding coding aspects of symbolic dynamics. We will begin with two sources of motivation: classification of classical dynamical systems and constraints on sequences recorded in data storage devices. These lead to similar coding problems that have been solved by symbolic dynamics. Then we will introduce the basic concepts of symbolic dynamics and survey some of the fundamental coding problems in the subject. (February 9) Vaughan Jones Planar Algebras The simplest planar algebra is the Temperley Lieb algebra which will be carefully defined as an algebra whose basis is a set of planar diagrams. Many algebras based on planar graphs are occurring and seem to play a vital role in the theory of subfactors. We will present some of these algebras. (February 16) Frank Morgan The Double Soap Bubble Conjecture The ancient Greeks suspected and Schwartz proved in 1884 that a round soap bubble provides the least-area way to enclose a given volume of air. The Double Bubble Conjecture says that the familiar double soap bubble is the least-area way to enclose and separate two given volumes of air. A proof for the case of two equal volumes was announced in August by Hass and Schlafly. The story has two remarkable features:

50. WPI Mathematical Sciences - Events 1999-2000 In both talks, he described recent results on the double bubble conjecture, whichsays that the familiar double soap bubble is the leastarea way to enclose http://www.wpi.edu/Academics/Depts/Math/News-Events/events,99-00.html

1999-2000 Events Commencement Click here for more photos. Mathematical Sciences Awards Ceremony Marcus Sarkis , and a team composed of Jovanna Baptista, Larissa Gilbreath, and Robert Jaeger received the CIMS MQP Award for their project "Pricing a Waiver of Premium Upon Disability," advised by Ann Wiedie and sponsored by John Hancock Insurance Company . Other participating teams and their projects were Andre Freeman and Matthew Lavoie, "Comparing Heuristics for the Traveling Salesman Problem," advised by Brigitte Servatius , and Elizabeth Hogan and Nicholas Allgaier, "Credibility Analysis for Automobile Cession Strategies," advised by Arthur Heinricher and sponsored by Premier Insurance of Massaschusetts. Jonathan Moussa and Matt Shaw were recognized for their strong performance on the Putnam exam, and two teams composed of Brian Ball , Jonathan Moussa, and James Stickney and Jon Kennedy, Will Kennerly, and Casey Richardson, respectively, were recognized for honors received in the COMAP 2000 Mathematical Contest in Modeling. See news item Undergraduates score in Math Modeling, Putnam competitions

51. WPI Mathematical Sciences - Colloquia 2000-2001 Frank Morgan, Mathematics Department, Williams College, March 24 2000 Title Thedouble bubble conjecture 1100 am, Stratton Hall, Room 203; refreshments at 10 http://www.wpi.edu/Academics/Depts/Math/News-Events/colloqdetail99-00.html

1999-2000 Colloquia Peter Smereka, Department of Mathematics, University of Michigan, April 28 2000 Title: Relaxation in Hamiltonian Systems 11:00 a.m., Stratton Hall, Room 203; refreshments at 10:30 a.m. in the department lounge, SH107. David Cai, Courant Institute of Mathematical Sciences, April 21 2000 Title: Dispersive Wave Turbulence and Energy Transfer Cycles 11:00 a.m., Stratton Hall, Room 203; refreshments at 10:30 a.m. in the department lounge, SH107. Barbara Keyfitz, John and Rebecca Moores University Scholar Department of Mathematics, University of Houston (currently visiting the Mathematics Department at Brown University), April 14 2000 Title: Solving Hyperbolic Problems with Elliptic Methods 11:00 a.m., Stratton Hall, Room 203; refreshments at 10:30 a.m. in the department lounge, SH107. Frank Morgan, Mathematics Department, Williams College, March 24 2000 Title: The Double Bubble Conjecture 11:00 a.m., Stratton Hall, Room 203; refreshments at 10:30 a.m. in the department lounge, SH107. Student Talk: News on the Double Bubble Conjecture, including work by undergraduates

52. Stanford University Geometric Analysis Seminar 1999-2000 April 19 Michael Hutchings, Stanford University Title The double bubble conjectureAbstract The double bubble conjecture states that the leastarea way to http://math.stanford.edu/~moore/ga-sem99-00.html

Stanford University Geometric Analysis Seminar 1999-2000 Unless otherwise noted, all seminars begin at 4:00 pm in room 380-381T, and last approximately one hour. There is tea at 3:30 in the lounge area on the third floor of the Math Department Building (Building 380). Spring 2000 Schedule March 29 Tobias Ekholm, Stanford University Title: Total curvatures of holonomic links Abstract: April 5 Jingyi Chen, University of British Columbia, Vancouver, Canada Title: Holomorphic connections and lagrangian cycles Dinner: We will be taking the speaker out to dinner at a nearby restaurant after the seminar. April 12 Dan Ostrov, Santa Clara University Title: Determining shapes from discontinuous shading data and solving related first order PDEs where the flux function is discontinuous Abstract: Shape from shading is the study of how to determine a 3-D surface from a 2-D picture of the surface (plus as minimal an amount of additional information as possible.) When the picture has discontinuities (i.e., a bright part of the picture borders a darker part), difficulties arise in determining existence, uniqueness, and a method of computation for the solution of the underlying PDE describing the surface. We will explain a method of resolving these questions involving a control theory representation for the PDE, which will also allow us to answer larger questions about much more general first order PDEs with discontinuous flux/Hamiltonian functions. Dinner: We will be taking the speaker out to dinner at a nearby restaurant after the seminar.

53. EXN.ca | Discovery Now, mathematicians at Williams College have proved the double bubble conjecture. Using a relatively simple mathematical formula, they showed this is indeed http://www.exn.ca/Stories/2000/03/20/54.asp

window.open('/message.asp','message','height=300,width=400,scrollbars=no,resizable=no'); EXN Science Wire: Daily news from the world of science By Discoverychannel.ca Staff , March 20, 2000 In today's stories: A new theory on climate change Bubbling with answers Making phone calls thanks to mirrors A new theory on climate change On Monday, a new take on the causes of global climate change emerged from the Proceedings of the National Academy of Sciences. Researchers studying ice and sedimentary core records say they've identified a new climate cycle - one that repeats every 1,800 years. They say it's related to the lunar tides. It's thought that tidal forces cause cooling at the sea surface by vertically mixing the oceans. If the idea is correct, it would mean that global warming predicted over the next few decades would be the result of a natural warming trend that began at the end of the last Ice Age. The warming trend would continue into the 32nd century. And, according to the research, it would produce warmer conditions than the Earth has seen in the past millennium. Bubbling with answers A lot toil and trouble has gone into understanding the double bubble and now there are some answers. For years, mathematicians have wondered why ordinary soap bubbles act the way they do. When two round bubbles come together, they form a double bubble, with the surface between them bowing a bit into the larger bubble. The angle between the two surfaces is always 120 degrees. The assumption has been that this is the optimum shape for the bubbles to take. Now, mathematicians at Williams College have proved the "double bubble conjecture." Using a relatively simple mathematical formula, they showed this is indeed the most efficient shape for enclosing two chambers of air. They also proved why other bubble formations don't appear in nature.

54. Kempner Colloquium Abstracts Title Proof of the double bubble conjecture Speaker Frank Morgan AffiliationWilliams College Time 230pm, Friday, April 2 Location EDUC 220 Abstract http://euclid.colorado.edu/~rmg/kempner/abstracts.html

Kempner Colloquium Abstracts Spring 2004 Title: Constructing Wavelets from Generalized Filters Speaker: Kathy Merrill Affiliation: The Colorado College Time: 4:15pm, Monday, January 12 Location: BESC 180 Abstract: Over the past twenty years, wavelets have gained popularity as bases for transforms used in image and signal processing. This talk will begin with a brief introduction to how wavelets arise naturally in this context. We will then show how the tools of abstract harmonic analysis and spectral multiplicity theory can be used to build and classify wavelets. In particular, we present results from joint work with L. Baggett, P. Jorgensen, H. Medina and J. Packer that extend the classical techniques of Mallat and Meyer to construct wavelets using generalized multi-resolution analyses and generalized filters. Title: Computing limiting stationary distributions of small noisy networks Speaker: Fred Richman Affiliation: Florida Atlantic University Time: 4:15pm, Monday, January 26 Location: BESC 180 Abstract: The dynamics of opinion transformation is modeled by a neural network with a nonnegative matrix of connections. Noise is introduced at each site, and the limit of the stationary distributions of the resulting Markov chains as the noise goes to zero is taken as an indication of what configurations will be seen. An algorithm for computing this limit is given, and a number of examples are worked out. Some of the mathematical ideas developed, such as visible states, time scales, and a calculus of indexed probabilities, are of independent interest.

55. Bubble Bubble page You can download here the preprint Proof of the double bubble conjecture ,by Michael Hutchings, Frank Morgan, Manuel Ritor?and Antonio Ros, 2000. http://www.win.it/ricerca/b/bubble_bubble.html

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56. Page014 March 2001 The double bubble conjecture is a true statement in dimension 4 Thiswas proved by the undergraduate students Ben Reichardt, Cory Heilmann, Yvonne http://www.math.utoledo.edu/~jevard/Page014.htm

Mathematical events (In reverse chronological order) Page maintained by Jean-Claude Evard. Last update: June 9, 2003. May 13, 2003: The Strong Perfect Graph Conjecture: Update by Gérard Cornuéjols: Link April 23, 2003: The breakthrough in the direction of the twin prime conjecture announced on March 13, 2003, does not hold. Andrew Granville of the Universite de Montreal and K. Soundararajan of the University of Michigan have found an error in the preprint Small gaps between primes of Daniel Goldston and Cem Yildirim. Additional information: 1. See announcement of the error on the Web site of the American Institute of Mathematics Link 2. See description of the error on the Web site of the American Institute of Mathematics Link 3. Article by Glennda Chui published in the Mercury News of May 7, 2003 Link 4. See Current Research on the Web site of Daniel Goldston Link April 16, 2003: The Poincare Conjecture seems to be on the edge to be solved: In an article published in the Moscow Time, Sara Robinson reports that Grigory Perelman, from the Steklov Institute of Mathematics in St. Petersburg

57. STUDENT PAPERS: SCHEDULE The recently proved double bubble conjecture says that the familiar double soap bubbleis the leastarea way to enclose and separate two regions of prescribed http://www.providence.edu/mcs/fpf/maa/fall03/moreabstracts.htm

Student Papers: Schedule Speaker and Title Time Room Brian D. Ginsberg Yale University The Nearly Secret Theorem of E. Midy – An Extension after 165 Years Elizabeth Bellenot, Wellesley College Effects of Biological Invasions on Ecological Communities Jessica S. Lee Wellesley College Mersenne Primes Michael J. Coleman Boston University and Sidharth Rupani WPI Modeling iBOT Belt Dynamics Seila Selimovic Wellesley College Who Wins: The Mathematician or The Physicist? The Dirac Delta function and Its Use in Quantum Mechanics Iuli Pascu Wellesley College A Graphical Interpretation for Complementary Sequences Karin Steece Wellesley College The Chinese Postman Problem XinXin Du Wellesley College Monte Carlo Simulations on One Electron Per Site, Two-Dimensional Square Lattices Paula F. Popescu Wellesley College Games with Hats Kathleen Leahy College of the Holy Cross Enigma – The Code that Changed History Charlie Rossetti and Matthew Angelucci Bentley College Dynamica Brandon Dwyer Bentley College A Student’s Look at the First Actuarial Exam Jenny Kirouac Westfield State College Naming Really Large Numbers Kari Lock Williams College Making Best Approximates Appear Through Magical Intervals Neil Hoffman Williams College Double Bubbles in Other Universes Speaker and Title Time Room Kathleen Smith Norwich University Vertex Total Magic Labelings Jerzy Wieczorek Olin College Solving ‘Rubik’s Polyhedra’ Using Three-Cycles

58. Math Coffees Frank Morgan of Williams College talk on The Proof of the double bubble conjectureand The Soap Bubble Geometry Contest at 4 pm and 730 pm, respectively, on http://www.davidson.edu/math/frontpage/Math_Coffees-02-03.htm

Faculty Courses Programs Math Center ... Student Job Opportunities Math Coffees Bernard Review Bernard Lecture [ Math Coffees ] Problem Contest Math Coffees Math Coffees are weekly meetings of students and faculty to hear a local or visiting speaker. The 2002-2003 Math Coffee season concluded with an outstanding session provided by this spring's MAT 118 class. Thanks to all our speakers and presenters this year. Check this space again in the fall for announcements of more great talks. MAT 118 Poster Session Exploring Mathematical Ideas 4 p.m.5 p.m., Thursday, May 1, Chambers 125 Explore with the students from Dr. Neidinger's Mathematics 118 class, Exploring Mathematical Ideas Spring 2003 Math Coffee Schedule (click on an image at the left to view the Math Coffee announcement) January 23 CANCELLED , Wake Forest University A Liberal Arts Approach to Mathematical Modeling January 30 45 p.m. Come hear one of the candidates for our mathematics faculty position talk on A Problem from the Game SET (TM) February 3 45 p.m.

59. Elsevier (Australia) This third edition of Geometric Measure Theory A Beginner s Guide presents, forthe first time in print, the proofs of the double bubble conjecture and the http://www.elsevier.com.au/book.cfm?id=70989

60. Project Euclid Journals Michael Hutchings, Frank Morgan, Manuel Ritoré, and Antonio Ros. Proofof the double bubble conjecture. Source Ann. of Math. 155 (2002), no. http://projecteuclid.org/Dienst/UI/1.0/Display/euclid.annm/1032210020

Current Issue Past Issues Search this Journal Editorial Board ... Subscriptions Michael Hutchings Frank Morgan , and Antonio Ros Proof of the double bubble conjecture Source: Ann. of Math. Abstract: Primary Subjects: Full-text: Open access Download the full-text in the following format: PDF (278 KB) Euclid Identifier: euclid.annm/1032210020 Current Mathmatical Publications number (MathSciNet): To Table of Contents for this Issue journals search login ... home

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