Column
- Math
Alphamagic Squares
Magic squares have fascinated people for thousands of years. They consist of a set of whole numbers arranged in a square so that the sum of the numbers is the same in each row, in each column, and along each diagonal. Some magic squares have special properties, such as using only consecutive numbers. In ancient […]
- Math
Theorems in Wheat Fields
It’s no wonder that farmers with fields in the plains surrounding Stonehenge, in southern England, face late-summer mornings with dread. On any given day at the height of the growing season, as many as a dozen farmers are likely to find a field marred by a circle of flattened grain. This close-up of a crop […]
- Math
Prime-Time Cicadas
Cicadas are flying, plant-eating insects. Most cicada species have life cycles that span 2 to 8 years. They spend most of their lives underground before emerging as adults. In a few species, almost all the individuals in a given location come out of hiding at the same time. These are known as periodical cicadas, and […]
- Math
A Dog, a Ball, and Calculus
Some dogs live to play fetch, especially if the object of interest is a favorite tennis ball or toy. Others, like ours, fetch only when the reward is a particularly tantalizing tidbit. At least one dog, however, appears to take the enterprise seriously enough to figure out an optimal path to the target. Elvis and […]
- Math
A Dog, a Ball, and Calculus
Some dogs live to play fetch, especially if the object of interest is a favorite tennis ball or toy. Others, like ours, fetch only when the reward is a particularly tantalizing tidbit. At least one dog, however, appears to take the enterprise seriously enough to figure out an optimal path to the target. Elvis and […]
- Math
Measuring with Jugs
Given a 5-liter jug, a 3-liter jug, and an unlimited supply of water, how do you measure out exactly 4 liters? In her book In Code: A Mathematical Journey, Sarah Flannery gives this classic brainteaser as an example of the sorts of playful puzzles that her father, a mathematics lecturer at the Cork Institute of […]
- Math
Deciphering the Wrinkles of Crumpled Sheets
Crumpling is a ubiquitous, though poorly understood, physical phenomenon. It occurs when a fender absorbs the energy of a car crash, when Earth’s crust buckles at the interface between colliding tectonic plates to create a mountain range, when a blood cell’s membrane folds to allow the cell to pass through a narrow capillary, when a […]
- Math
Sequence Puzzles
Given a sequence consisting of the whole numbers 1, 4, 9, 16, 25, 36, and 49, what number comes next in the sequence? The most likely answer is 64–the next number in a sequence of squares of consecutive integers, starting with 1. Such sequence puzzles are a staple of textbook exercises, brainteaser collections, and various […]
- Math
Coins for Making Change Efficiently
The item I had just bought cost 29 cents. I gave the cashier a dollar bill, and she gave me two quarters, two dimes, and a penny in change. She could just as well have given me seven dimes and a penny or some other combination of coins adding up to 71 cents, but there’s […]
- Math
A Geometric Superformula
The notion of a simple equation that you can use to generate a wide variety of geometric shapes is an immensely appealing one. Johan Gielis of Antwerp, Belgium, proposes one such formula in the March American Journal of Botany. “Many geometrical forms, both in nature and culture, can be interpreted as modified circles,” Gielis states. […]
- Math
Recycling Topology
It’s hard to miss the triangle of three bent arrows that signifies recycling. It appears in newspapers and magazines and on bottles, envelopes, cardboard cartons, and other containers. The recycling symbol. Alternative (incorrect?) rendering of the recycling symbol. Cliff Long made a Möbius band the basis of his wood carving “Bug on a Band.” Photo […]
- Math
The Colors of an Equation’s Roots
Over the centuries, mathematicians have developed a variety of methods of solving equations. Using the capabilities of modern computers, they have explored in detail how these age-old recipes work–when the methods can be relied upon, when they fail, and when they behave strangely. A polynomiograph of a degree-36 polynomial. B. Kalantari “Cathedral” by B. Kalantari. […]
