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 ...
Published:
2001-02-08 10:09:27
Found in: Numbers
In a book completed in the year 1202, mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second month on?The total number of pairs, month by month, forms the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. Each new term is the sum of the previous two terms. This set of numbers is now called the Fibonacci sequence.The Fibonacci numbers, F[x] (starting with 0), display a variety of patterns, inc...
Published:
2001-02-08 15:24:25
Found in: Numbers
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...
Published:
2001-02-08 16:14:15
Found in: Numbers
The famous Mesopotamian clay tablet known as Plimpton 322 represents an ordered list of worked examples that a teacher would use to prepare a sequence of closely related questions about squares and reciprocals for student exercises. (p. 56)
Found in: Numbers
Even with perfect play over a long time, unfavorable odds and limits on how much a gambler may win per machine make playing video poker into a losing game. (p. 56)
Found in: Numbers
Researchers in theoretical computer science have made progress in settling the question of whether a clairvoyant scheduler can regulate the timing of moves by random walkers on a grid to keep them from ever colliding. (p. 36)
Found in: Numbers
Anyone trying to refold an opened road map is wrestling with the same sort of challenges confronted by origami designers and sheet metal benders.The problem of returning a creased sheet to its neatly folded state gets tougher when you're not sure if the sheet can be folded into a flat packet and when you're not permitted to change the crease directions. Such conundrums can arise, for example, when designers determine how to bend sheet metal to produce, say, car doors, airplane parts, or heating ducts.Now Erik D. Demaine of the computer science department at the University of Waterloo in Ontari...
Published:
2001-01-12 11:35:39
Found in: Numbers
Anyone trying to refold an opened road map is wrestling with the same sort of challenges confronted by origami designers and sheet metal benders.The problem of returning a creased sheet to its neatly folded state gets tougher when you're not sure if the sheet can be folded into a flat packet and when you're not permitted to change the crease directions. Such conundrums arise, for example, when designers determine how to bend sheet metal to produce, say, car doors, airplane parts, or heating ducts.Now, Erik D. Demaine of the computer science department at the University of Waterloo in Ontario a...
Published:
2001-01-08 17:07:34
Found in: Numbers