81. Mathematicians Prove Double Soap Bubble Had It Right Four mathematicians have announced a mathematical proof of the double bubbleConjecture that the familiar double soap bubble is the optimal shape for http://www.sciencedaily.com/releases/2000/03/000320090849.htm

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 ... Outdoor Living Source Williams College Date Print this page Email to friend Mathematicians Prove Double Soap Bubble Had It Right WILLIAMSTOWN, Mass., March 18, 2000 Four mathematicians have announced a mathematical proof of the Double Bubble Conjecture: that the familiar double soap bubble is the optimal shape for enclosing and separating two chambers of air. What's Related Clotting Cells Switched On By Cold Champagne And Bubbles: Smaller Is Better Are The Digits Of Pi Random? A Berkeley Lab Researcher May Hold The Key related stories Related sections: In an address to the Undergraduate Mathematics Conference at the Rose-Hulman Institute of Technology in Indiana on Saturday (March 18), Frank Morgan of Williams College announced that he, Michael Hutchings of Stanford, and Manuel Ritori and Antonio Ros of Granada had finally proved that the double soap bubble had it right all along.

82. News Letter Soap bubble Theorem. This talk will focus on the 2002 result showing that the familiardouble soap bubble is the least Poincare conjecture Lecture Series. http://www.math.tcu.edu/Newsletters/Archive/Sept03/News.html

TCU Math News Letter Volume 12, Number 1 September 2003 The mind is not a vessel to be filled, but a flame to be kindled - Plutarch Editor: Dr. Rhonda Hatcher and Archive of Newsletters Green Honors Chair Visit, September 21-23 Professor Frank Morgan of Williams College will be visiting the Mathematics Department at TCU as the Green Honors Chair. He will be on our campus from Sunday, September 21 through Tuesday, September 23. Professor Morgan will present four talks during his visit. His first talk, a public lecture entitled 'Soap Bubbles and Mathematics,' will be at 4:00 p.m., Sunday, September 21 in Sid Richardson Building, Lecture Hall 2. He will report on soap bubbles in the recent math news, followed by a guessing contest with demonstrations, explanations, and prizes. The talk is open to everyone (4th grade and above). Refreshments will be served after the talk. Lunchtime talks by Professor Morgan, with free pizza and drinks provided, are scheduled for Monday, September 22 and Tuesday, September 23 at 12:00 noon in Tucker Technology Center 139. The Monday talk, 'Pizzas, Bubbles, and other Isoperimetric¹ Shapes,' will include a discussion of some results proved by undergraduates. The Tuesday talk, 'Double Bubbles in Other Universes,' will explore the question of what double soap bubbles should look like in other universes. This talk will also include results by students and open questions. On the afternoon of Monday, September 22 at 4:00 p.m. Professor Morgan will present the talk 'The Double Soap Bubble Theorem.' This talk will focus on the 2002 result showing that the familiar double soap bubble is the least-perimeter way to enclose and separate two given volumes. Refreshments will be served in TTC 300 at 3:30 p.m.

83. American Scientist Online - A Lucid Interval Hass, Joel, Michael Hutchings and Roger Schlafly. 1995. The double bubbleconjecture. Electronic Research Announcements of the AMS 195–102. http://www.americanscientist.org/template/AssetDetail/assetid/28331/page/6;_roe_

Home Current Issue Archives Bookshelf ... Subscribe In This Section Search Book Reviews by Issue Issue Index Topical Index ... Classics Site Search Advanced Search Visitor Login Username Password Help with login Forgot your password? Change your username see full issue: November-December 2003 Volume: Number: Page: DOI: COMPUTING SCIENCE Other Formats: PDF Postscript Postscript (gzipped) A Lucid Interval Intervals at Work G , done with two pendulums attracted to large brass weights. The interval analysis assessed various contributions to the uncertainty of the final result, and discovered a few surprises. An elaborate scheme had been devised for measuring the distance between the swinging pendulums, and as a result this source of error was quite small; but uncertainties in the height of the brass weights were found to be an important factor limiting the overall accuracy. Would we be better off if intervals were used for all computations? Maybe, but imagine the plight of the soldier in the field: A missile is to be fired if and only if a target comes within a range of 5 kilometers, and the interval-equipped computer reports that the distance is [4,6] kilometers. This is rather like the weather forecast that promises a 50-percent chance of rain. Such statements may accurately reflect our true state of knowledge, but they're not much help when you have to decide whether to light the fuse or take the umbrella. But this is a psychological problem more than a mathematical one. Perhaps the solution is to compute with intervals, but at the end let the machine report a definite, pointlike answer, chosen at random from within the final interval.

84. You Can’t Hear The Shape Of A Drum (Carolyn Gordon Et Al by 1993. http//www.pbs.org/wgbh/nova/proof/wiles.html. double BubbleConjecture Proved (Michael Hutchings et al. 2000). The double http://www.mathsci.appstate.edu/mathclub/math.html

Some Recent Mathematical Results and Open Problems Worth a Million Dollars$$$$$$$!! In 1966 the mathematician Mark Kac asked the question, Can you hear the shape of a drum? That may seem like a strange question at first, but it's no stranger than asking if one can ``see'' the chemistry of a star. In the 1991 solution, mathematicians came up with examples of drums that have different shapes but have exactly the same characteristic vibration frequencies. You wouldn't hear any difference if you listened to these drums with your eyes shut tight. http://www.ams.org/index/new-in-math/hap-drum/hap-drum.html In the margin of a book, next to the statement that x n + y n = z n I have discovered a truly remarkable proof which this margin is too small to contain http://www.pbs.org/wgbh/nova/proof/wiles.html Double Bubble Conjecture Proved (Michael Hutchings et al. 2000) The double soap bubble on the left is the optimal shape for enclosing and separating two chambers of air (a given volume) using the least amount of material (surface area). In 1995 the special case of two equal bubbles was heralded as a major breakthrough on this problem when proved with the help of a computer. The new general case involves more possibilities than computers can now handle. The new proof uses only ideas, pencil, and paper. http://www.maa.org/features/mathchat/mathchat_3_18_00.html

85. The Math Major Vol. 1, No. 13 Dr. Hass, with his collaborator Roger Schlafly, proved last year the double BubbleConjecture which answered a question that had been first asked 2000 years http://zimmer.csufresno.edu/~larryc/mathmajor/vol1/v1n13.html

The Math Major CSU Fresno Mathematics Department Vol 1. No. 13 (Last Issue for Spring Semester) Editor: Dr. Larry Cusick Math Department Colloquium Schedule This colloquium was originally scheduled for March 17, but was postponed. Speaker: Dr. Joel Hass, UC Davis Title of Talk: Double Bubbles Minimize Location: S 145 Abstract: Dr. Hass will be speaking about the mathematical models of soap films and bubbles, which are modeled by minimal surfaces and constant mean curvature surfaces respectively. Dr. Hass, with his collaborator Roger Schlafly, proved last year the "Double Bubble Conjecture" which answered a question that had been first asked 2000 years ago and had been studied by many great mathematicians throughout history. He will be speaking about some of the innovative techniques used in this important work and will have some computer graphics as well as soap bubbles to illustrate the ideas. Sixteenth CSU, Fresno Math Field Day: A Success On Saturday April 19, the CSUF math department hosted the Math Field Day for high schools. There were 11 high schools represented by approximately 200 students. Students competed in mathematical competitions that required problem solving skills to tackle difficult math problems. Edison high school received the top award. Second place was Dinuba high school. The department would like to thank the CSU Fresno student volunteers and the staff of the math department office who helped make the event possible. Education Loans (From Dr. Tuska) Applications for the Assumption Program of Loans for Education (APLE) are currently available in Room 100 of the Education Building. If selected for this program, students will have up to $8,000 in student loans repaid by the California Student Aid Commission. These applications must be returned to Room 100 no later than Friday, May 2, 1997 by 5:00p.m. Contact the School of Education for more information and the minimum requirements.

86. Math Trek: Bubbles And Math Olympiads, Science News Online, June 16, 2001 Last summer, Andrew Cotton and David Freeman proved the double bubbleconjecture for equal volumes in hyperbolic and spherical space. http://www.sciencenews.org/articles/20010616/mathtrek.asp

Math Trek Bubbles and Math Olympiads Food for Thought Allergic to computing? Science Safari Geo Name Game TimeLine 70 Years Ago in Science News Week of June 16, 2001; Vol. 159, No. 24 Bubbles and Math Olympiads Ivars Peterson Predicting the geometric shapes of soap bubble clusters can lead to surprisingly difficult mathematical problems. 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 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."

87. Frank Morgan At MSRI - Geometric Measure Theory And The Proof Of The Double Bubb Frank Morgan Geometric Measure Theory and the Proof of the DoubleBubble conjecture - Lecture 5. MSRI Streaming Video Series Frank http://elasmo.kaist.ac.kr/ln/msri/2001/minimal/morgan/4/

MSRI Streaming Video Series Frank Morgan - Geometric Measure Theory and the Proof of the Double Bubble Conjecture - Lecture 5

88. Frank Morgan At MSRI - Geometric Measure Theory And The Proof Of The Double Bubb Frank Morgan Geometric Measure Theory and the Proof of the DoubleBubble conjecture - Lecture 8. MSRI Streaming Video Series Frank http://msri.mathnet.or.kr/ln/msri/2001/minimal/morgan/8/

MSRI Streaming Video Series Frank Morgan - Geometric Measure Theory and the Proof of the Double Bubble Conjecture - Lecture 8

89. Frank Morgan At MSRI - Geometric Measure Theory And The Proof Of The Double Bubb Frank Morgan Geometric Measure Theory and the Proof of the DoubleBubble conjecture - Lecture 9. MSRI Streaming Video Series Frank http://msri.mathnet.or.kr/ln/msri/2001/minimal/morgan/9/

MSRI Streaming Video Series Frank Morgan - Geometric Measure Theory and the Proof of the Double Bubble Conjecture - Lecture 9

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