Math Trek
- Math
Hyperbolic Five
Dutch graphic artist M.C. Escher (1898–1972) devised many highly original schemes in his attempts to capture the concept of infinity visually. One strategy he often employed was to create repeating patterns of interlocking figures. However, although he could imagine how such arrays extended to infinity, the actual pattern he drew represented only a fragment of […]
- Math
SET Math
The card game known as SET® is deceptively simple. Its object is to identify, as quickly as possible, a grouping (SET) of three cards, selected from 12 cards laid out face up on a table. A SET deck has 81 (34) cards. Each card displays a design with four attributes: shape, number, shading, and color. […]
- Math
Golf Clubs and Driving Distance
The last 20 years have seen remarkable changes in golf equipment: metal-headed drivers, forgiving irons, new putter variants, juiced golf balls, and more. Have these technology changes led to improved performance? Anecdotal evidence certainly points to such improvements. In 1980, for example, the leader in driving distance on the Professional Golfers of America (PGA) Tour […]
- Math
Running Lanes and Extra Steps
When going out to your local running track for a workout, you sometimes find that you are allowed to use only certain lanes for training. On any looped track, however, the outer lanes are longer than the inner lanes. That presents a problem for someone using the track for speed workouts. A four-lane equal-quadrant running […]
- Math
Perfect Pyramids
The tetrahedron is the simplest of all polyhedra—solids bounded by polygons. It has four triangular faces, four vertices, and six edges. If each edge has the same length and each face is an equilateral triangle, the result is a regular tetrahedron—one of the Platonic solids. Example of a tetrahedron. Another group of tetrahedra that some […]
- Math
Perfect Pyramids
The tetrahedron is the simplest of all polyhedra—solids bounded by polygons. It has four triangular faces, four vertices, and six edges. If each edge has the same length and each face is an equilateral triangle, the result is a regular tetrahedron—one of the Platonic solids. Example of a tetrahedron. Another group of tetrahedra that some […]
- Math
Improving the Odds in RISK
RISK is a classic board game of global conquest. First published in 1959, this war game remains a popular pastime–and continues to attract mathematical attention. Recent analyses reveal that the chances of winning a battle are considerably more favorable for the attacker than was originally suspected. “The logical recommendation is . . . for the […]
- Math
Improving the Odds in RISK
RISK is a classic board game of global conquest. First published in 1959, this war game remains a popular pastime–and continues to attract mathematical attention. Recent analyses reveal that the chances of winning a battle are considerably more favorable for the attacker than was originally suspected. “The logical recommendation is . . . for the […]
- 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 […]
