There are few places in the world where you can raise your right hand in front of your Secretary of State and swear to do
your country proud by teaching mathematics. Zimbabwe happened to be one of them. The Peace Corps sent eight math teachers
there in 1997 as part of a group of almost forty volunteers. I am one-eighth of that story.
Finding Centroids the Easy Way
Archimedes (287-212 B.C.), often called the greatest mathematician of ancient times, created the concept of centroid,
which he used in many of his writings on mechanics. But we can only speculate on what he had in mind when he referred
to centroids because none of his extant works provides an explicit definition of the concept.
From Oz to Earth
Professor Wogglebug was once an ordinary tiny bug. As the Royal Historian reveals in The Marvelous Land of Oz, the bug
hid in the warm hearth of a school where Professor Nowitall taught. To show his students what a wogglebug looked like,
he put the bug in a projector and threw his image on a large screen.
The Traveling Baseball Fan
In the summer of 1980, Rick Cleary and Mike Chuba had just finished Master's degrees in mathematics and they wanted to do
a little traveling. Both were avid baseball fans so they decided to see a game in every major league ballpark. With
a limited budget and no reliable car, Rick and Mike chose to get around the country by bus. Gathering some helpful
friends, road maps, baseball schedules and bus schedules, they spent an afternoon coming up with a plan that would get
them to each of the ball parks over a period of about seven weeks.
Student Research at the Joint Meetings
We wandered into the ballroom of one of the conference hotels on Friday night during last winter's national mathematics
meeting in Washington, DC. It was a mob scene! We could barely hear one another and making progress through the thick
crowd was difficult; clearly the Undergraduate Research Poster Session was the place to be.
A Dozen Areal Maneuvers
Your dozenal correspondent is at it again! This time I have put together a collection of twelve curiosities all to do
with areas, and, in some cases, the perimeters that contain them. The questions about slicing pie and cake are technically
ones about volumes, but we'll assume here all desserts are of uniform thickness so they may be reduced solely to
analysis of area. Many of these results are classic (one even known by Archimedes) but hopefully the few extra twists
I've put in shine these gems in a new and interesting light. I hope you have as much fun thinking about these as I did.
Problem Section
S-43.
Proposed by Mircea Ghita, Stuyvesant High School. Solve the equation for all real x: 1 + 2^{x+1} + 3^x + 5^x +
7^x = 8^x.
S-44.
Proposed by P. Wagner, Chicago, IL. Two known properties of hyperbolas are: (i) If perpendicular segments are drawn
from any point on the curve to its two asymptotes, the product of the lengths of these segments is constant. (ii) If any
line intersects the curve and its two asymptotes in the four consecutive points A, B, C, D, then AB = CD. Prove that
any curve with two intersecting straight line asymptotes and having either of the above properties must be a hyperbola.
S-45.
Proposed by Linda Eroh (graduate student) and Allen J. Schwenk, Western Michigan University. A game of Jai Alai has eight
players and starts with players P_1 and P_2 on court and the other players P_3, P_4, P_5, P_6, P_7, P_8 waiting in a queue.
After each point is played, the loser goes to the end of the queue; the winner adds 1 point to his score and stays on
the court; and the player at the head of the queue comes on to contest the next point. Play continues until someone
has scored 7 points. At that moment, we observe that a total of 37 points have been scored by all eight players.
Determine who has won.
The Final Exam: Madison Avenue Mathematics
From 1927 until well into the 60's, families on vacation scouted the roadsides, not for the Golden Arches, but for a
5-element sequence of little signs, reading something like:
Past schoolhouses
Take it slow
Let our little
Shavers grow
BURMA SHAVE
Burma Shave is the brand name of a shaving cream, reportedly sweet smelling and making shaving much more convenient.
The signs, strategically spaced, could only be read one at a time, so there was an element of suspense as each line was
revealed. It was a brilliant advertising campaign, winning brand recognition among, well, almost everyone who could read.
