Column

Math

Folding Paper in Half—Twelve Times

You can’t fold a sheet of paper in half more than seven or eight times, no matter how large the sheet or thin the paper may be. How often have you heard that statement? Perhaps you’ve even put this assertion to the test. And, indeed, it is difficult to get beyond about seven or eight […]

Math

Extreme Tides

If Earth had been somewhat larger, it’s possible that it would not have survived tides induced by its moon or even by an encounter with a passing asteroid. That’s one scenario suggested by a recent investigation of a venerable equation that serves as a model for planetary tidal effects. Tidal effects are caused by the […]

Math

Splitting Terrorist Cells

How can you tell if enough members of a terrorist cell have been captured or killed so there’s a high probability that the cell can no longer carry out an attack? A mathematical model of terrorist organizations might provide some clues. The question is what sort of mathematical model would work best. In this hypothetical […]

Math

Perfect Magic Cubes

A magic cube is a three-dimensional array of whole numbers, in which each row, column, and body diagonal (corner to corner, through the center) adds up to the same total. A perfect magic cube is one in which the diagonals of each vertical or horizontal slice through the cube also sum to the same value. […]

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 […]