Ptolemys Theorem
Ptolemy's Theorem states that if a quadrilateral is cyclic, then the product of the lengths of the diagonals equals th…
Decisive Decades: Celebrating The Closing Century
A glance at the major time periods in the history of mathematics reveals a picture of many dimensions. Inspiring momen…
21 Problems For The Twenty-First Century
The dawning of the twenty-first century provides a rare opportunity for looking ahead, a time of speculating, and a ch…
The Modern Geometry of the Triangle Revisited
Members of my senior mathematics course produced the following article. The course was an attempt by the class to make…
How To Male A Log Table: A Flagrant Exercise In Atavism
Imagine that you're stranded on a desert island and want to make a table of logarithms.Why, for heaven's sakes? That's…
Fundamental Theorem of Algebra Part II: The Theorem's Proof, The Theorem's Impact
From the times of the late Renaissance, the theory of equations was characterized in western culture by a high level o…
Fundamental Theorem of Algebra Part I: The Theorem Foreshadowed
A far-reaching discovery in the late 1700s was to secure, even more so, the closing century's remarkable standing in t…
The Postage Stamp Problem
When Hugh Burkhardt visited Teachers College a few years ago, he began his lecture with the following problem: Imagine…
Reversals of Genetic Fortunes
The last couple of decades have witnessed a thorough mixing of mathematics, computers, and biology. This mixing has re…
Drugs and Blocks
When your doctor prescribes a new drug or treatment (medical or surgical), your hope is that the condition that requir…
Trees, Chains, and Chances
The relatively new field of bioinformatics is undergoing explosive growth. Even before the current impetus provided by…
Partitions: Numbers As More Than The Sums Of Their Parts
Despite the advice of his advisor that he choose a more modest problem to solve for his dissertation, a young graduate…
Mathematics Helps Sort Out Our Genes
One area of intense contemporary activity in applied mathematics is mathematical biology. Advances in the study of man…
It's A Small World
Many people, in one context or another, are familiar with the "small world" phenomenon. You're sitting next to a stran…
One Egg or Two? Statistics Helps Shed Light on Paleontology Mystery
One of the goals of paleontology is to connect what we learn through fossil records of extinct animals' biology to the…
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. Wh…
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 st…
Tunnel Vision
In the traditional trigonometry course, no problem is more time-honored than the tunnel problem. What is it? A compete…
Mathematics: A Myriad of Methods (Part 2)
Demonstrative mathematics, dating from the Early Greek Era, has a long and continuing history, and characterizes the G…
Reflection
What follows is a direct result of the work I have been doing over the past five years on a National Science Foundatio…
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 situ…
Curves Ahead
The following article was written by several students in my computer graphics class. I have added some diagrams and th…
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 solu…
Did You Know That ...?
Little known facts often surface by an extended probing of the historical record. These may be revelations of subtle c…
Humorous Historical Highlights
There's very little to smile about in algebra class. Or geometry, trigonometry, and whatever else may align with that…
In ' Plane ' View
This article was produced as an assignment for a computer graphics course that I am currently teaching to high school…
The Lemma Dilemma
Various proofs in the history of mathematics have necessitated an incredible number of steps. Some, because of step si…
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 think…
Nothing Really Important
Great events in world history are not always acknowledged as such nor appreciated at the time of occurrence. It is oft…
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 Canto…
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 in…
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 propor…
What - More Logarithms?!
The question this time concerns the use of logarithms in mathematical modeling. You will argue that this is so common…
Mathematics: From Recreation to Application
Recreational mathematics, that branch of the discipline that refreshes one's spirit, is admittedly a difficult area to…
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 " ques…