All Stories by Ivars Peterson
- Math
The EKG Sequence
Sequences of numbers have long fascinated both amateur and professional mathematicians. Many people are familiar with the Fibonacci sequence, in which each new term is the sum of the previous two terms: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. More than 69,000 other sequences of interest to mathematicians […]
- Math
Guessing Secrets
Analyzing an intriguing variant of the familiar game of 20 questions provides insights into Internet communication.
- Math
Rainbow Randomness
The branch of pure mathematics known as Ramsey theory concerns the existence of highly regular patterns in sufficiently large sets of randomly selected objects, whether they are gatherings of people, piles of pebbles, stars in the night sky, or sequences of numbers generated by the throw of a die. Jacob Licht Patterns can arise out […]
- Math
Highway Relativity
There may be more to zipping along in the fast lane than meets the casual eye. Freeway drivers often sense that cars in an adjacent lane are moving faster than those in their own lane. That’s certainly true when the average speed of the cars in the next lane is significantly higher than that of […]
- Math
Highway Relativity
There may be more to zipping along in the fast lane than meets the casual eye. Freeway drivers often sense that cars in an adjacent lane are moving faster than those in their own lane. That’s certainly true when the average speed of the cars in the next lane is significantly higher than that of […]
- Math
Scrabble’s Random Letters
In the popular SCRABBLE Brand Crossword Game, players create words from letters selected at random from a stockpile of 100 tiles. The tiles are laid down on a board 15 squares high by 15 squares wide to form an interlocking, crossword arrangement. Each letter of the alphabet has a particular value and the number of […]
- Math
Scrabble’s Random Letters
In the popular SCRABBLE Brand Crossword Game, players create words from letters selected at random from a stockpile of 100 tiles. The tiles are laid down on a board 15 squares high by 15 squares wide to form an interlocking, crossword arrangement. Each letter of the alphabet has a particular value and the number of […]
- Math
Ice Cream Wars
A visit to the supermarket can present a shopper with a bewildering array of choices. For ice cream alone, the consumer faces a variety of brands, flavors, container sizes, and types (fat-free versus low-fat versus premium, and so on). At the same time, deciding which items to stock is a formidable problem for retailers. They […]
- Math
A Snowy Twist
Carving a massive block of packed snow into an elegant sculpture presents all sorts of challenges. It’s even tougher when the goal is an intricate mathematical shape with a gravity-defying heart. A Twist in Time. Photo by Stan Wagon Eltanin by Bathsheba Grossman. On display at the northeast corner of 33rd and Walnut St., University […]
- Math
Algebraic Hearts
One of the marvels of mathematics is the way in which an austere equation can unexpectedly blossom into an appealing geometric shape when represented graphically. Cardioid. Picture of an algebraic heart. Gabriel Taubin A heart surface colored according to Gaussian curvature (left) and direction (right). Michael Trott/Wolfram Research A heart-y prime puzzle. Ed Pegg Jr. […]
- Math
Euler’s Homework
Even the best and most prolific of mathematicians have had to do homework assignments. Famed Swiss mathematician Leonhard Euler (1707–1783) was no exception. Euler was only 14 years old when he was sent to the University of Basel in 1720 to study for the ministry. Not long after his arrival, he got himself introduced to […]
- Math
Sampling for Superclarity
An audio compact disc (CD) holds up to 74 minutes, 33 seconds of music, just enough for a complete recording of Ludwig van Beethoven’s Ninth Symphony on one disc. Each second of music is stored as a string of about 1.5 million bits, represented as tiny, narrow pits on the disc’s surface. These pits range […]
