All Stories by Ivars Peterson
- Math
Defending the Roman Empire
Years ago, when I was in high school and college, the board games Risk and Diplomacy served as wonderful playing fields where I could develop and exercise my tactical and negotiating skills. One issue that often came up in my forays into international intrigue was how to deploy my limited forces to defend far-flung territories […]
- Math
Möbius at Fermilab
Fermilab’s Wilson Hall. Courtesy of Fermilab. Soaring into the sky like a medieval cathedral, the twin towers of the structure known as Wilson Hall dominate the flat countryside surrounding the Fermi National Accelerator Laboratory (Fermilab) in Batavia, Ill. Named for physicist and accelerator builder Robert Rathbun Wilson (1914-2000), the building celebrates Wilson’s vision and skill, […]
- Math
Solving Yahtzee
Sometimes described as poker with dice, Yahtzee is an immensely popular game. Its manufacturer, Hasbro, claims that as many as 100 million people worldwide play the game regularly. Yahtzee involves rolling five dice with the aim of obtaining favorable scoring combinations. For example, rolling five of a kind scores 50 points, whereas rolling three of […]
- Math
Scrambled Grids
Amazingly simple mathematical operations can lead to intriguingly complex results. Consider, for instance, the iterative geometric process of creating flaky pastry dough. Flatten and stretch the dough, then fold it over on top of itself. Do it again and again and again. Repeating the pair of operations–stretch and fold–just 10 times produces 1,024 layers; 20 […]
- Math
Goldbach’s Prime Pairs
Like the elements in chemistry, prime numbers serve as building blocks in the mathematics of whole numbers. Evenly divisible only by themselves and one, primes are a rich source of speculative ideas that mathematicians often find simple to state but difficult to prove. The Goldbach conjecture is a prime example of such a conundrum. In […]
- Math
Software’s Origin
One of the main functions of the venerable and massive Oxford English Dictionary is to record the earliest known use of a word (or sense of a word) in English. The current edition of the dictionary dates the word software back to 1960, though researchers have discovered an 1850 occurrence of the term in a […]
- Math
Software’s Origin
One of the main functions of the venerable and massive Oxford English Dictionary is to record the earliest known use of a word (or sense of a word) in English. The current edition of the dictionary dates the word software back to 1960, though researchers have discovered an 1850 occurrence of the term in a […]
- Math
Art of the Grid
The practice of laying a grid on top of a drawing, then painstakingly copying each line of the drawing to the corresponding cell of a blank grid seems old-fashioned in these days of pervasive photocopying and electronic image manipulation. Nonetheless, the underlying idea of transferring information from one grid to another has a long history […]
- Math
Contra Dances, Matrices, and Groups
Though unknown to many people, contra dancing is practiced with great devotion and abandon throughout the United States by fans of this lively dance form. What’s striking is that a remarkably high percentage of contra dancing’s practitioners are highly educated, often involved in mathematics, computers, or engineering. Matrix representing initial configuration of two couples in […]
- Math
Turtle Tracks
One way to describe a geometric figure is in terms of the path generated by a moving point. Instead of defining a square, for example, as a four-sided polygon with equal sides and angles, you can call it the path generated by the following rule: Go straight for a distance s, turn 90 degrees right, […]
- Math
Cracking Fermat Numbers
Fermat numbers have what mathematicians sometimes describe as a “beautiful mathematical form,” involving powers of 2. They were of interest 400 years ago and are now the subject of a wide-ranging worldwide computer search. A Fermat number has the form 22n + 1, where n is a whole number equal to or greater than 0. […]
- Math
The Tangled Task of Distinguishing Knots
Consider the plight of a gardener struggling with a recalcitrant tangle of garden hose. Sometimes, no amount of pulling or twisting unsnarls the coils. At other times, the tangles readily come apart, and the hose emerges unknotted. Trefoil knot. Different views of the figure-eight knot. Robert Scharein Braid (left) and its closed form (right). Robert […]
