FOCUS May/June 2000 FOCUS is published by the Mathematical Association of America in January, February, FOCUS March, April, MaylJune, August/September, October, November, and December. May/June 2000 Editor: Fernando Gouvea, Colby College; [email protected] Volume 20, Number 5 Managing Editor: Carol Baxter, MAA [email protected] Inside Senior Writer: Harry Waldman, MAA [email protected] 4 General Double Bubble Conjecture in R3 Solved By Joel Hass Please address advertising inquiries to: Carol Baxter, MAA; [email protected] 6 MAA Professional Development Workshops Summer 2000 President: Thomas F. Banchoff, Brown University 7 Have You Met Everybody ... ? First Vice-President: Barbara L. Osofsky, Second Vice-President: Frank Morgan, By Nora Franzova Secretary: Martha J. Siegel, Associate Secretary: James J. Tattersall, Treasurer: 8 Finding Your Second (and Third ... ) Job Gerald J. Porter By sarah-marie belcastro and Michael Prophet Executive Director: Tina H. Straley Associate Executive Director and Director 9 bmovative Programs Address Professional Development of Teaching of Publications and Electronic Services: Assistants & Adjuncts Donald J. Albers By Teri ]. Murphy et al. FOCUS Editorial Board: Gerald Alexanderson; Donna Beers; J. Kevin 11 Short Takes Colligan; Ed Dubinsky; Bill Hawkins; Dan Kalman; Maeve McCarthy; Peter Renz; Annie Selden; Jon Scott; Ravi Vakil. 12 Standards Based Education By Robby Robson and M. Paul Latiolais Letters to the editor should be addressed to Fernando Gouvea, Colby College, Dept. of Mathematics, Waterville, ME 0490 I. 14 MAA and Tensor Foundation Announce New Awards Subscription and membership questions By Florence Fasanelli should be directed to the MAA Customer Service Center, 800-331-1622; e-mail: 16 Preliminary Announcement for Contributed Papers for [email protected]; (301) 617-7800 (outside New Orleans U.S. and Canada); fax: (301) 206-9789. 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Editorial Copy July 14 September 15 Display Ads July 28 August 21 October 6 Employment Ads July 21 August 10 September 22 2 May/June 2000 FOCUS Georgia Benkart Named 2000-01 P61ya Lecturer MAA Earmarks Funds The MAA's On a rotating basis, the MAA sections can for Student Activities Board of invite any of the current P6lya lecturers By Tina H. Straley Go v ern 0 r s to speak at a regional meeting. The award has selected includes a stipend and covers the travel The MAA is earmarking all revenues G e 0 r g i a expenses involved in attending the sec- generated by the MAA Visa Card to sup­ Benkart, of tion meetings. The scheduling of specific port student activities at the Section level. the Univer- lectures is done by the Committee on Sec- Since 1989, the Exxon Education Foun­ sity of Wis- tions, which is chaired by David Stone. dation has awarded the MAA annual consin, grants to support a variety of student ac­ Madison, as Past P6lya lecturers were John Ewing, tivities. These activities, which have in­ the newest Patricia Rogers, Carl Pomerance, Robert cluded the MAA Student Lecture, Student Georgia Benkart, new George P6lya Osserman, Underwood Dudley, Laszlo Workshops, and special paper and poster George P6lya Lecturer. Lecturer. She Babai, and Ronald Graham. Currently, sessions at national meetings, have in­ will serve for two lecturers, Colin Adams (1998-99, creased student participation in MAA the academic years 2000-01 and 2001-02. 1999-00) and Joseph Gallian (1999-00, meetings and in mathematics in general. 2000-01), are visiting the Sections .• Unfortunately, the newly formed Exxon/ Mobil Corporation has informed us that Thomas Rishel Named Associate Executive they are no longer able to support stu­ dent activities, so MAA has been actively Director for Programs and Services pursuing an alternative source of fund­ ing. Thomas graduate Teaching and as Senior Lecturer Rishel, from in the department of mathematics. The MAA's activities and programs for Cornell students are an important part of the University, Rishel's service to the MAA includes Association's service to the mathemati­ will become chairing its Task Force on Graduate Stu­ cal community. Our programs foster the the MAA's dents and as a member of the MAA Task development of tomorrow's mathemati­ Associate Force on Institutional Membership as cal pioneers and leaders. In order to con­ Executive well as a member of the AMS-MAA Joint tinue to be able to fund these programs, Director for Committee on Employment Opportuni­ the MAA has earmarked all revenue gen­ Member ties. He is also the chair of the Selection erated by the MAA credit card (backed Services Committee of the MAA Professors for by MBNA Bank) for use in student ac­ Thomas Rishel, new Asso­ and Pro­ the Future Program and is active in the tivities. I hope that you continue to sup­ ciate Executive Director for grams in Seaway Section. port MAA's student activities by using MAA Member Services July 2000. your MAA credit card, or obtaining one and Programs. Rishel is the author of The Academic Job if you don't already have one. For infor­ Rishel holds Search, published by the AMS; A Hand­ mation on the MAA credit card call 1- a doctorate from the University of Pitts­ book for Mathematics Teaching Assistants: 800-847-7378. Promo code: E4CB .• burgh and has published papers about Preliminary Edition, an MAA publica­ c-spaces and Morita's M spaces. He has tion; and Writing in the Teaching and Tina H. Straley is the Executive Director spent the last twenty years at Cornell Learning of Mathematics, an MAA pub­ of the Mathematical Association of University as the Director of Under- lication in the MAA Notes Series .• America. Proposed Fiscal 2001 Budget Calls for $2.8 Billion Increase in Science R&D President Clinton's budget for Fiscal proposal, with a requested increase in its Have You Moved? Year 2001, which he submitted to Con­ budget of $675 million, or 17.3 percent. gress in early February, includes a $2.8 Mathematical programs at the Depart­ The MAA makes it easy to change your billion increase for scientific research and ment of Energy (DOE) would also receive address. Please inform the MAA Service development across all federal agencies significant increases, while the request for Center about your change of address and disciplines. the Department of Defense's basic re­ by using the electronic combined mem­ search accounts would fare less well. The bership list at MAA Online (http:// New funding is directed at the core pro­ President's request will be evaluated by www.maa.org) or call (800) 331-1622, grams of mathematical research at the Congress over the next few months. See fax (301) 206-9789, email National Science Foundation (NSF) and http://www.maa.org/features/ [email protected], or mail to MAA, other government agencies. The NSF budgetOO.html for an analysis of the pro­ P.O. Box 90973, Washington, DC 20090. would benefit under the current budget posed budget. • FOCUS May/June 2000 General Double Bubble Conjecture in R3 Solved By Joel Hass components are enclosed the shape as­ Each surface in this bubble has constant sumed is known as a "standard double mean curvature, or constant average In March 2000, the proof of the general bubble." This is made of pieces of three bending. This corresponds to a constant double bubble conjecture in R' was an­ round spheres, meeting along a common pressure difference between the two re­ nounced by four mathematicians: circle at an angle of 120· as in Figure 1. gions the surface separates. Constant Michael Hutchings of Stanford Univer­ The double bubble conjecture asserts that mean curvature surfaces are very special, sity, Frank Morgan of Williams College, this shape is the most efficient one pos­ but far too general to classify. In a com­ and Manuel Ritore and Antonio Ros of sible in enclosing two given volumes. plicated soap froth, each piece of surface the University of Granada. Their proof More precisely, if VI and V2 are two has constant mean curvature, and can be completes a long history of work on the specified volumes, the conjecture is that far more complicated than just a piece of problem. the surface enclosing these volumes and a sphere. Fortunately, the surfaces used having smallest possible area is a standard in constructing an optimal two region Since early farmers started to fence off double bubble. The special case where bubble are very special. White, Foisy and fields and beer drinkers started to design VI =V 2 was established earlier [HHSJ. Hutchings applied symmetry arguments clay tankards, people have pondered how Hutchings, Morgan, Ritore and Ros have to show that the optimal double bubble to enclose as much as possible within a now established the double bubble con­ is a surface of revolution-it is symmet­ container. The Greeks dubbed these jecture for all volumes. ric under rotation around an axis. The "isoperimetric" (same perimeter) prob­ possible configurations now become trac­ lems. Zenodorus made the first known Here is a sketch of the proof. The first is­ table, and Hutchings established that attempt to show that the circle is the sues that occur are existence and regu­ there was a rather limited number of pos­ shortest curve in the plane enclosing a larity.