Search

Modern dynamics began with Galileo's investigations of the motion of projectiles in a nonresisting medium. Galileo ingeniously compounded the accelerated vertical motion of a projectile (obtained from his law of falling bodies) with its unaccelerated horizontal motion (an expression of his principle of inertia) to conclude that the path of the projectile is parabolic. Projectile motion is now a prime application in virtually every calculus text. Indeed, the power of analytic geometry and calculus, along with the elements of Newton's dynamics, has reduced Galileo's great achievement to a mere exercise. If a projectile of unit mass is projected from the origin at an angle 0 with the horizontal with initial speed v, under the influence of a uniform gravitational acceleration g, then the equations of motion

An international team of mathematicians has announced a proof of the "double bubble" conjecture, which states that when two soap bubbles come together, they form a double bubble in order to enclose the total volume with the minimum surface area. By honing a new technique for analyzing the stability of competing shapes, the team has shown that only the standard shape is truly minimal--any other, supposedly area-minimizing shape can be ever so slightly twisted into a shape with even less area, a contradiction that rules out these other candidates.

At the Joint Mathematics Meetings, researchers reported the first sightings of "perfect parallelepipeds," bricks whose sides are allowed to be parallelograms rather than strict 90o rectangles and all 13 of whose edges and diagonals are exact integers. Their search used computer algorithms to build candidate parallelepipeds and then winnow out the "perfect" ones.

JOINT MATHEMATICS MEETING, 13–16 JANUARY, SAN FRANCISCO, CALIFORNIAAt the Joint Mathematics Meetings, mathematical voting theorists described a recent case study that suggests different voting systems only rarely produce the vastly different results possible in theory. An analysis of ranked ballots from 8 years of voting for the presidency of the American Psychological Association showed that different voting methods gave the same result much more often than not.

MATHEMATICSPhysicists have long sought an exact mathematical solution to the Ising model, a powerful tool for studying phase transitions--the abrupt changes of state that occur, for instance, when ice melts or cooling iron becomes magnetic--because it would provide much more information about such still-mysterious transitions. Now a theoretical computer scientist has proved that the Ising model--at least in its most general, three-dimensional form--belongs to a class of problems that theorists believe will remain unsolved forever.

What did the groundbreaking modernist painter Marcel Duchamp learn from Henri PoincarA©, the father of chaos? Historians of art and science, along with mathematicians and postmodern theorists, debated the question from 5 to 7 November at a conference organized by Rhonda Roland Shearer, a New York City-based artist, and her husband, Harvard biologist Stephen Jay Gould (who is also the president of AAAS, which publishes Science). Shearer and her colleagues have gathered evidence that Poincarean ideas lurk behind several of the artist9s most famous works--and as a result, these works are not what they appear to be.

> MATHFEST 2008, 31 JULY-2 AUGUST, MADISON, WISCONSIN In 1850, the great German mathematician Carl Friedrich Gauss took a shine to a funky little counting problem: How many ways can eight queens be placed on a chessboard so that no two queens attack one another (i.e., line up horizontally

GEOMETRY AND THE IMAGINATION PRINCETON, NEW JERSEY--At a meeting held here on 7-11 June in honor of the mathematician William Thurston, geometer Richard Schwartz showed that a game of "outer billiards"--in which point-sized balls graze the corners of a geometric target--can result in orbits that spiral outward forever.

SAN DIEGO —At the joint meetings of the American Mathematical Society and the Mathematical Association of America here, a historian of mathematics shed new light on how mathematical research survived the Cultural Revolution in China during the 1960s and '70s. A highly abstract theory imported from the capital of Western imperialism, the United States, helped Chinese mathematicians cast their work in an ideologically favorable light, he said.

MAP LAUNCHWhat links the cosmic microwave background (CMB) to the grand structure of the universe is the fabric of space-time. But just what is that fabric, and what can CMB measurements tell us about it?