Like toy cars chasing each other on a looped racetrack, three stars can, in principle, trace out a figure-eight orbit in space. This newly discovered, mathematically surprising pattern of motion arises from the force of gravity acting on three bodies of equal mass. Their movements are timed so that each body in turn passes between the other two.Newton’s laws provide a precise answer to the problem of determining the motion of two bodies under the influence of gravity. If the solar system consisted of the sun and a single planet, for example, the planet would follow an elliptical orbit. When th...

Like toy cars chasing each other on a looped racetrack, three stars can, in principle, trace out a figure-eight orbit in space. This newly discovered, mathematically surprising pattern of motion arises from the force of gravity acting on three bodies of equal mass. Their movements are timed so that each body in turn passes between the other two.Newton’s laws provide a precise answer to the problem of determining the motion of two bodies under the influence of gravity. If the solar system consisted of the sun and a single planet, for example, the planet would follow an elliptical orbit. When th...

Computer programs can handle all sorts of data, from sums of money in bank accounts to sensor readings from scientific instruments. In many cases, the data are a set of discrete elements, such as temperatures. Moreover, some elements of a set may be larger in value than others, or they may exhibit some other relationship that allows you to rank them or put them in order.In mathematics, such a collection of elements is known as a partially ordered set, or poset. One example of a poset consists of an integer and all its positive divisors (excluding 1). For instance, the positive divisors of 42 a...

Anyone who has waited for a bus in the city has probably casually observed that, after an inordinately long wait, two or three buses often come along at the same time.The question of why such bunching seems to happen has prompted all sorts of speculation. Some claim that bus bunching is actually a rare occurrence, but passengers tend to forget the much larger number of times when a single bus arrives. Others posit that bus drivers simply like to travel in packs.Mathematical models that simulate traffic flow confirm that bus bunching is a real phenomenon. Even though buses leave their depot at...

"Need a zero-volume bottle? Searching for a one-sided surface? Want the ultimate in nonorientability?"The intriguing subject of these cryptic entreaties is a bizarre mathematical object known as a Klein bottle, discovered in 1882 by German mathematician Felix Klein (1849-1925).An ordinary bottle has an inside and an outside. To walk from the inside to the outside, a fly would have to cross the lip that forms the bottle's mouth. A Klein bottle has no such edge. What appears to be its inside is continuous with its outside.One way to describe a Klein bottle is in terms of instructions for making ...

The elegant, swooping forms carved out of wood by sculptor Robert Longhurst often resemble gracefully curved soap films that span twisted loops of wire dipped into soapy water. Alhough these abstract sculptures bear an uncanny resemblance to mathematical forms known as minimal surfaces, they emerge from Longhurst's imagination rather than from mathematics."Curvilinear works, whether they fall into the categories of art, architecture, or design, have always held a fascination for me beyond that of straight lines," Longhurst says.Trained as an architect, Longhurst has been carving wood and stone...

Juggling competing demands in a network of feverishly calculating computers drawing on the same memory resources is like trying to avert collisions among blindfolded, randomly zigzagging ice skaters.Among networked computers, some sort of software scheduler must act as a referee to regulate data flow. Proving that a given scheduler not only prevents conflicts but also performs its duties efficiently can be surprisingly difficult, however. Computer scientists have found that analyzing even simple data-sharing cases can be troublesome.One important scheduling problem is equivalent to moving two ...

Juggling competing demands in a network of feverishly calculating computers drawing on the same memory resources is like trying to avert collisions among blindfolded, randomly zigzagging ice skaters.Among networked computers, some sort of software scheduler must act as a referee to regulate data flow. Proving that a given scheduler not only prevents conflicts but also performs its duties efficiently can be surprisingly difficult, however. Computer scientists have found that analyzing even simple data-sharing cases can be troublesome.One important scheduling problem is equivalent to moving two ...