Until very recently, most Bush toilets were controlled by a mechanism whose workings were filled with differential poetry. In the rear tank of the toilet was a bulbous metal Boat, budding in hues of oxidation at the end of a gently curving metal stem....
Political scientists who study comparative government have charted a staggering variety of legislative systems. In designing these different systems, countries have the common goals of fairness, efficiency, and stability, as well as goals that are...
Farmer Klaus and the Mouse [Goßen and Rubin 1997] is a cooperative board game for children ages 3 and up that has both chance and strategy aspects. We use mathematical analysis-specifically, the technique of dynamic programming-to determine how often...
While preparing to perform a piece of music, a pianist must work out a fingering for the piece. Sometimes, the optimal fingering is obvious and emerges naturally during sight-reading. Other times, when the easiest fingering is unclear, the sheet music...
In almost any country in the world, it would be of considerable interest to many quarters in society to know how the human population of that country will or may evolve in the future. Such knowledge would influence greatly a multitude of decisions and...
There is an old Latin proverb, common in translation in Germany, that "Those who live closest to the church arrive last" ("Proximus ecclesiae semper vult ultimus esse.") At first glance, this has a nice air of paradox about it: Why should those who are...
As part of the promotion for its new Berry Berry Kix cereal, General Mills included on the cereal box a game called "Berry Patch Scramble," which turns out to be a pretty good game for children or mathematicians. It has elements in common with the...
The most significant mathematical development in 1994 occurred near the end of the year, when Andrew Wiles (Princeton University) presented a revised proof of Fermat's last theorem, a year and a half after his first announcement of a proof and almost a...
The year 1995 was a relatively quiet one in mathematics. Mathematicians confirmed and celebrated the revised proof by Andrew Wiles of Princeton University of Fermat's Last Theorem. An even more ancient problem was solved when researchers proved that a...
After several years of suspense and excitement about the proof of Fermat's last theorem, the achievements in 1996 were not as spectacular as those of previous years, yet they were still surprising in their own way. A computer proved a mathematical...
Mathematics in 1997 was marked by the celebration of achievements and by the contemplation of philosophical questions and computational results. The Nobel Prize for Economics was awarded for a mathematical model formulated in the 1970s that is crucial...
Mathematics in 1998 saw the resolution, at last, of Johannes Kepler's simple sounding conjecture about sphere-packing; an explanation for the "small world" phenomenon; a mathematical theory for origami, the Japanese art of paperfolding; and a new...
We give an example, using first-year calculus and least-squares curve-fitting, of the use of mathematical modeling in chemical reaction engineering. Little previous knowledge of chemistry is required. Reaction engineering involves "the exploitation of...
While students versed in mathematics are often exposed to methodologies involved in solving mathematical models, less often do they see integrated models that utilize constructs across disciplines, each dependent upon mathematics for the development of...
The concept of "comfort" has so many complications and implications that there is no hope of finding a global scientific model to describe it; to "feel comfortable" is the result of human reactions, physical characteristics, design aspects,...
A large theme park presents its guests with an interesting and challenging problem: choosing rides to visit and an order in which to visit them. To solve this problem, visitors must balance profits (enjoyment obtained from rides) and costs (time spent...
Before this decade, interest in ice hockey moved at glacier speed from Canada and across the United States. Now professional leagues have expanded into regions of the United States in which natural ice is rarely seen, such as the Louisiana Ice Gators,...
In 1975, Jacob Eli Goodman posed the following problem in the American Mathematical Monthly under the pseudonym of Harry Deweighter ("harried waiter"): The chef in our place is sloppy, and when he prepares a stack of pancakes they come out all...
Determining winning strategies for the game of Chessboard Trichrome is an open problem appearing in Silverman [1991]. Chessboard Trichrome is a two-player game played on an 8 X 8 chessboard with red, black, and white kings. Players alternately place a...
Error-correcting methods are used when some binary message digits (bits, with values 0 or 1) switch value during transmission. To enable correction of errors, extra check digits are sent with the message digits, expanding the message word to a longer...