Math Trek
- 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, […]
- Math
The Bias of Random-Number Generators
Some popular random-number generators fail even in simulating a coin toss.
- Math
Rolling with Reuleaux
Have you ever wondered why the cover of a manhole is nearly always round? Why isn’t it oval or square? Reuleaux curve based on an equilateral triangle. Reuleaux curves based on the pentagon (top) and heptagon (bottom). The usual answer is that a circular lid, unlike a square or an oval cover, won’t fall through […]
- Math
Trimathlon Palindromes
“A man, a plan, a canal–Panama.” This statement is a famous example of a palindrome–a phrase that reads the same forward or backward. Inventive wordsmiths and puzzlists have come up with all sorts of words, sentences, and even paragraphs that have this property. The term palindrome can also be applied to whole numbers, such as […]
- Math
Pennant Races and Magic Numbers
It’s getting close to the end of the regular baseball season. Fanatic fans track not only which team is in first place or in position for a wild-card berth in the playoffs but also the number of games a team must win to avoid elimination. The elimination, or “magic,” number is usually defined to be […]
