Numerical Fulcrums: Providing Leverage for Work with Primes
What might be a numerical fulcrum? Consider the sequence of consecutive
positive integers 1, 2, 3, 4, 5, 6, 7, 8. ...
Taking the Temperature of Mathematical Problems: What Makes Some Hard?
Take a glass of water at room temperature and cool it by a few degrees centigrade. Consider the changes in the water...
A Long Way from Home: Transatlantic Sea Star Migration
For a marine biologist strolling along the eastern coast of South America, finding some sea stars (popularly called ...
Tunnel Vision
In the traditional trigonometry course, no problem is more time-honored than the tunnel problem. What is it? A compe...
Mathematics: A Myriad of Methods (Part 2)
Demonstrative mathematics, dating from the Early Greek Era, has a long and continuing history, and characterizes the...
Reflection
What follows is a direct result of the work I have been doing over the past five years on a National Science Foundat...
That's A Wrap!
In this issue of Consortium, we start a series of Henry's Notes that concern the interaction between a real-world si...
Curves Ahead
The following article was written by several students in my computer graphics class. I have added some diagrams and ...
Mathematics: A Myriad of Methods (Part 1)
A famous problem may have many solutions. The primary goal in any encounter with a challenging problem is that of so...
Did You Know That ...?
Little known facts often surface by an extended probing of the historical record. These may be revelations of subtle...
Humorous Historical Highlights
There's very little to smile about in algebra class. Or geometry, trigonometry, and whatever else may align with tha...
In ' Plane ' View
This article was produced as an assignment for a computer graphics course that I am currently teaching to high schoo...
The Lemma Dilemma
Various proofs in the history of mathematics have necessitated an incredible number of steps. Some, because of step ...
Air a Mathematical Model of Defense
Mathematical thinking about air defense is a subject whose acceptability varies a lot. But if you are willing to thi...
Nothing Really Important
Great events in world history are not always acknowledged as such nor appreciated at the time of occurrence. It is o...
Crises In Mathematics (Part 2): A Raging Tempest
Beyond non-Euclidean geometries, one of the earliest encounters with completeness was that of the works of Georg Can...
The ABC's of Point Count Systems
When I have taught the unit on Social Choice, one of the questions that sometimes arises concerns the numbers used i...
Crises In Mathematics (Part 1): A Gathering Tempest
Mathematics, throughout the many pages of history, has had its bright and dismal moments. Crises, some of major prop...
What - More Logarithms?!
The question this time concerns the use of logarithms in mathematical modeling. You will argue that this is so commo...
Mathematics: From Recreation to Application
Recreational mathematics, that branch of the discipline that refreshes one's spirit, is admittedly a difficult area ...
Scenario: The Mathematics of Presidential Elections
Number notions underlying the election of the president of the United States can be the source of many "what if " qu...
History Condensed To A Year
Time perspectives are often gained by various comparisons to the highly familiar. Landmark events in the eons of the...
Some Thoughts On Applications Of Polynomials
Elementary applications for the mathematics of polynomials have historically tended to emphasize either the physics ...
Calendar Cryptology
The sending and deciphering of secret messages is today referred to as cryptology, a term stemming from a Greek work ...
With Compass & Straightedge in Hand
Quite early in the classroom pursuit of Euclidean geometry, students learned how to construct the highly familiar ri...
Postcard Collecting
One of my minor vices-some would call it an addiction-is that I am a collector. One of my collections is of lithograp...
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...