Tetrahedral Treats
Have you ever wondered about the geometry of tetrahedra? It would seem that there should be some fascinating results...
A Mathematical Paradise (The World of Infinity) Part II
Many of the unsolved problems of today concern the question "How many?" Various number sets are obviously finite, su...
How To Build A Box
We begin with the following question: Isit possible to construct a perfect cubical box from six identical pieces of ...
What Is a Regular Polygon?
The answer to this question must seem so obvious that regular readers of this periodical will assume there has to be...
A Mathematical Paradise (The World of Infinity) Part I
When a daring question's true answer proves vastly out of line with centuries of conventional thought, still deeper ...
Drawing A Triangle
It happened to me-again- last semester. I needed to draw an "arbitrary" triangle on the blackboard. I did not want i...
Elegant Mathematics
Although the role of solid geometry in the secondary mathematics curriculum is sometimes minimal, many contemporary ...
A Bouncing Ball
Once again, we are looking at a problem in which the accuracy of the measurements, and the sensitivity of the calcul...
Mathematical Milestones
The history of mathematics is characterized by diverse lines of possible development. Perhaps the progressive accoun...
The Universality of Mathematics (Part 2: The Distant Scene)
The focus of the story of mathematics in western culture begins essentially with the Dawn of History (the appearance...
Why Does a Truck So Often Get Stuck in Our Underpass?
It just doesn't seem reasonable that trucks should have as much trouble as they do. After all, in every case I know,...
Getting A Better Angle
This month's column deals with one of my favorite problems. I originally found it in Heinrich Dorrie's 100 Great Pro...
Cellular Automata
Much of what we teach with regards to modeling is still very much influenced by the Newtonian deterministic view of ...
Hanging Pictures
In the two preceding issues we examined various possible happenings when you compare the accuracy of the conclusions...
The Universality of Mathematics (Part 1: The Greek Horizon)
The universal nature of mathematics leads the historian to consideration of far-flung geographical areas of growth a...
The Average of Rates and the Average Rate
In our everyday lives, we often hear phrases involving averages: the student has a grade-point average of 3.12, the ...
The Midge Problem
In 1989, the Mathematical Contest in Modeling offered a wonderful problem about distinguishing a "good" midge from a...
The Weather Forecaster Problem
Suppose you have two forecasts for tomorrow's weather. Forecast A predicts a 60% chance of rain, while Forecast B pr...
The Gerrymander Problem: Measuring Compactness
Every ten years, the U.S. House of Representatives is reconfigured according to the results of the U.S. Census. This...
The Hiring Problem
Anew wing has been added to the magnet school for Mathematics, Science, and Technology so that the student populatio...
The Gas Station Problem
Every driver recognizes the fluctuations in gas prices that happen almost on a weekly basis. In many areas, local ra...
Spread of an Infectious Disease
Last spring it was SARS.This winter it's the flu. In the spring it's SARS again and the avian flu.The spread of AIDS...
The Blood Testing Problem
Suppose that you have a large population you wish to test for a certain characteristic in their blood or urine (for ...
The Traffic Flow Problem
Everyone has at some time been on a multi-lane highway and encountered road construction that required the traffic t...
The Hot Dog Stand Location Problem
A map shows the walking paths and dormitories in a section of campus and the approximate distances (in 100 feet) bet...
Apportionment: Measuring Unfairness
Every ten years when the census is taken, the federal government rearranges or reapportions the delegates in the Hou...
Great Lakes Problem
Iteration and difference equations are beginning to play a significant role in high school mathematics. The Great La...
The Suez Canal
In the Suez Canal Problem, we consider the real-world, multimillion dollar question of traffic flow through the Suez...
Evaluating Modeling Solutions: The Art Gallery Problem
Mathematical modeling plays an important role in the high school mathematics program in Australia. As part of the fi...
How Many Taxis?
You are standing in the rain trying to hail a cab in a large city. While waiting, seven cabs pass by that already ha...
The Ferris Wheel Problem
This problem is designed for students in Algebra II and beyond. In order to make a start with this problem, students...
The Michael Jordan Problem
The Michael Jordan Problem is a subtle, but challenging problem for Advanced Algebra or Precalculus students. Every y...
Voting Power
In ordinary elections, each person has a single vote and everyone's vote has the same power. However, in some situat...
Measuring Inequity
The distribution of income in our society is a concept of ongoing interest to economists, politicians, public policy...
The Ladder Problem and Extension
This issue's problem comes from Ron Lancaster, of Saint Paul's School in Ontario, Canada. Ron presented this problem ...
The Irrigation Problem
This article has students imagine a linear irrigation system to uniformly spray water on a rectangular field where th...