【正文】 and surrealism, became more personally expressive. Jackson Pollock39。s turbulent yet elegant abstract paintings, which were created by spattering paint on huge canvases placed on the floor, brought abstract expressionism before a hostile public. Willem de Kooning39。s first oneman show in 1948 established him as a highly influential artist. His intensely plicated abstract paintings of the 1940s were followed by images of Woman, grotesque versions of buxom womanhood, which were virtually unparalleled in the sustained savagery of their execution. Painters such as Philip Guston and Franz Kline turned to the abstract late in the 1940s and soon developed strikingly original styles— the former, lyrical and evocative, the latter, forceful and boldly dramatic. Other important artists involved with the movement included Hans Hofmann, Robert Motherwell, and Mark Rothko。 among other major abstract expressionists were such painters as Clyfford Still, Theodoros Stamos, Adolph Gottlieb, Helen Frankenthaler, Lee Krasner, and Esteban Vicente. Abstract expressionism presented a broad range of stylistic diversity within its largely, though not exclusively, nonrepresentational framework. For example, the expressive violence and activity in paintings by de Kooning or Pollock marked the opposite end of the pole from the simple, quiescent images of Mark Rothko. Basic to most abstract expressionist painting were the attention paid to surface qualities, ., qualities of brushstroke and texture。 the use of huge canvases。 the adoption of an approach to space in which all parts of the canvas played an equally vital role in the total work。 the harnessing of accidents that occurred during the process of painting。 the glorification of the act of painting itself as a means of visual munication。 and the attempt to transfer pure emotion directly onto the canvas. The movement had an inestimable influence on the many varieties of work that followed it, especially in the way its proponents used color and materials. Its essential energy transmitted an enduring excitement to the American art scene. Science and technology is quite a broad category, and it covers everything from studying the stars and the plas to studying molecules and viruses. Beginning with the Greeks and Hipparchus, continuing through Ptolemy, Copernicus and Galileo, and today with our work on the International Space Station, man continues to learn more and more about the heavens. From here, we look inward to biochemistry and biology. To truly understand biochemistry, scientists study and see the unseen by studying the chemistry of biological processes. This science, along with biophysics, aims to bring a better understanding of how bodies work – from how we turn food into energy to how nerve impulses transmit. analytic geometry, branch of geometry in which points are represented with respect to a coordinate system, such as Cartesian coordinates, and in which the approach to geometric problems is primarily algebraic. Its most mon application is in the representation of equations involving two or three variables as curves in two or three dimensions or surfaces in three dimensions. For example, the linear equation ax+by+c=0 represents a straight line in thexyplane, and the linear equation ax+by+cz+d=0 represents a plane in space, where a, b, c, and dare constant numbers (coefficients). In this way a geometric problem can be translated into an algebraic problem and the methods of algebra brought to bear on its solution. Conversely, the solution of a problem in algebra, such as finding the roots of an equation or system of equations, can be estimated or sometimes given exactly by geometric means, ., plotting curves and surfaces and determining points of intersection. In plane analytic geometry a line is frequently described in terms of its slope, which expresses its inclination to the coordinate axes。 technically, the slope m of a straight line is the (trigonometric) tangent of the angle it makes with the xaxis. If the line is parallel to the xaxis, its slope is zero. Two or more lines with equal slopes are parallel to one another. In general, the slope of the line through the points (x1, y1) and (x2, y2) is given by m= (y2y1) / (x2x1). The conic sections are treated in analytic geometry as the curves corresponding to the general quadratic equation ax2+bxy+cy2+dx+ey+f=0, where a, b,?…?, f are constants and a, b, and c are not all zero. In solid analytic geometry the orientation of a straight line is given not by one slope but by its direction cosines, λ, μ, and ν, the cosines of the angles the line makes with the x, y, and zaxes, respectively。 these satisfy the relationship λ2+μ2+ν2= 1. In the same way that the conic sections are studied in two dimensions, the 17 quadric surfaces, ., the ellipsoid, paraboloid, and elliptic paraboloid, are studied in solid analytic geometry in terms of the general equationax2+by2+cz2+dxy+exz+fyz+px+qy+rz+s=0. The methods of analytic geometry have been generalized to four or more dimensions and have been bined with other branches of geometry. Analytic geometry was introduced by Ren233。Descartes in 1637 and was of fundamental importance in the development of the calculus by Sir Isaac Newton and G. W. Leibniz in the late 17th cent. More recently it has served as the basis for the modern development and exploitation of algebraic geometry. circle, closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone. The term circle is also used to refer to the region enclosed by the curve, more properly called a circular region. The radius of a circle is any line segment connecting the center and a point on the curve。 the term is also used for the length r of this segment, ., the mo