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.
Suppose You Want to Vote Strategically
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.
TopSpin on the Symmetric Group
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.
Spending the Weekend with a Model
Eric awoke from an early evening nap, remembering that he had a new project to start in a few hours. The Ghana native
zipped up his coat tightly, slipping across the Grinnell College campus on a typically cold Iowa evening in early February.
Just before midnight, he made his way to Professor Chamberland's office where a group of students were anxiously waiting.
The sixteenth annual Mathematical Contest in Modeling (MCM) was about to begin.
One Point Determines a Line
The Axiom of Choice states that if you've given a set of non-empty sets, then it is possible to choose an element from
each set. It follows that it is possible to choose a point from each and every straight line in the plane. But of
course the Axiom of Choice isn't necessary for this. For example, one might choose from each vertical line its
x-intercept, and from each non-vertical line its y-intercept. This choice function leaves a couple of things to be
desired: different lines correspond to the same point and some points don't correspond to any lines. What we seek is
a one-to-one and onto function from the set of all lines in the plane to the set of all points in the plane with the
additional property that if a line corresponds to a point, then that point lies on that line.
You DO Haiku
In the April 2000 issue of Math Horizons, the Final Exam "Do You Haiku?" challenged you to create your own mathematical
haiku, and send the results to us. We received 85 entries from across the country, including some from high school
students and teachers, college students and professors, and even entire classes and entire families tried their collective
hands at penning the perfect poem.
Ten out of Nine Dentists Prefer Crest...
One of the benefits of a sound mathematical/statistical education is the ability to distinguish plausible quantitative
information from that which is false or misleading. In today's information-overloaded world, information quantity often takes precedence
over quality. As a result, unreliable and misinformed statements by the media, by politicians, and across the Internet
are proliferating.
Getting the Job You Want
What makes the difference between a successful and an unsuccessful job candidate? How do you present yourself to
maximize your chances of being hired? When do you start preparing yourself for the job market?
Problem Section
S-46.
Proposed by Andy Liu, University of Alberta. ABCD is a convex quadrilateral and E, F, G, H, are the midpoints of AB, BC,
CD, DA, respectively. Prove that the area of ABCD is at most EG times FH.
S-47.
Proposed by the Problem Editor. Prove that (a^2 + b^2 + 1) >= (a^2 + b)^2 + (a + b^2)^2 + 1.
The Final Exam: World Wide Web Treasure Hunt
The Internet weaves an astronomical amound of information, a superfluity of shopping, and an embarrassment of useless
trivia, into its web. Have you ever wondered how to make a Cafe au Lait Luzianne? Do you need a map from Newton, Iowa to
Newton, Massachusetts? Have you ever wondered what sort of academic pedigree your favorite math professor has? Perhaps
you ponder the egg-laying capacity of the black widow spider. With a surprisingly small number of clicks, you can answer
these questions and more.
