【正文】 a circle is circumscribed about a polygon if all the vertices of the polygon lie on the circumference. The length of the circumference C of a circle is equal to π (see pi) times twice the radius distance r, or C=2πr. The area A bounded by a circle is given by A=πr2. Greek geometry left many unsolved problems about circles, including the problem of squaring the circle, ., constructing a square with an area equal to that of a given circle, using only a straight edge and pass。 the term is also used for the length r of this segment, ., the mon distance of all points on the curve from the center. Similarly, the circumference of a circle is either the curve itself or its length of arc. A line segment whose two ends lie on the circumference is a chord。 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。 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。 the harnessing of accidents that occurred during the process of painting。 the use of huge canvases。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。, and surrealism, became more personally expressive. Jackson Pollock39。s disease. abstract expressionism, movement of abstract painting that emerged in New York City during the mid1940s and attained singular prominence in American art in the following decade。 in glands, smooth muscle, and the heart they are ‘muscarinic’。 an enzyme (cholinesterase)