Column
- Math
Sculpting with a Twist
There’s more than one way to slice a bagel. A bagel (or a doughnut) can serve as a physical model for a mathematical surface called a torus. You can slice it horizontally (or longitudinally) so that you end up with two halves, each containing a hole. That’s great for making sandwiches because the cut exposes […]
- Math
Tricky Crossings
Have you heard the one about an itinerant entertainer traveling with a wolf, a goat, and a basket of cabbages? E. Roell The showman comes to a river and finds a small boat that holds only himself and one passenger. For obvious reasons, he can’t leave the wolf alone with the goat, or the goat […]
- Math
Megaprime Champion
The catalog of humongous prime numbers has a new entry–the champion prime (220996011 – 1), which has 6,320,430 decimal digits. It’s the largest known prime number and the 40th Mersenne prime ever found. A prime is a whole number (other than 1) that is evenly divisible by only itself and 1. Written in the form […]
- Math
The Cow in the Classroom
“Miss Zarves drew a triangle on the blackboard. ‘A triangle has three sides,’ she said, then pointed to each side. ‘One, two, three.’ She drew a square. ‘A square has four sides. One, two, three, four.’ “She walked around the cow to the other side of the board. She drew a pentagon, a hexagon, and […]
- Math
Pentomino Battleships
Many of you are probably familiar with the two-player, pencil-and-paper (or electronic) game known as Battleships. There are 12 different pentominoes, each one consisting of five adjacent squares. Traditionally, each pentomino is identified by the letter of the alphabet that it roughly resembles. On separate 10-by-10 grids of squares, each player deploys a fleet consisting […]
- Math
Cool Rationals
It’s curious how some classroom words, activities, or incidents can stick in your mind for years. I can still recall certain grammar rules from lessons long past, for example. When one of these rules comes into play as I write, I can remember not only the teacher’s words but also the tone and manner in […]
- Math
Geometreks
Strolling down a city street or along a country road can provide a geometrical feast for the eye—when the viewing is done from a mathematical perspective. National Gallery of Art, East Building. I. Peterson To fit the National Gallery’s East Building on a trapezoid-shaped site, architect I.M. Pei based his design on a division of […]
- Math
Strolling Down Möbius Lane
The Möbius band is a fascinating object. You can make a simple model of it by joining the ends of a long, narrow strip of paper after giving one end a 180-degree twist. The result is a one-sided, one-edged surface in the form a single closed continuous curve with a twist. A Möbius band. A […]
- Math
Seven-Game World Series
In professional baseball’s World Series, the championship is decided in a best-of-seven format. The first team to win four games gets the pennant. Curiously, series that go on for the full seven games appear to occur more often than simple probability arguments would suggest. Suppose that two, evenly matched teams have made it to the […]
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- Math
Goldbach Computations
In 1742, historian and mathematician Christian Goldbach (1690–1764) wrote a letter to Leonhard Euler (1707–1783) in which he suggested, in effect, that every integer greater than 5 is the sum of three prime numbers. A prime number is evenly divisible only by itself and 1. Nowadays, Goldbach’s conjecture is expressed in the following equivalent form: […]
- Math
A Magic Knight’s Tour
For as long as chessboards have existed, there have been puzzles involving chessboards and chess pieces. Some of the most enduring conundrums involve knights. Example of a knight’s tour in which the rows and columns have the same sum (260), but the diagonals add up to 348 and 168. According to the rules of chess, […]
