By Wang Defu, Qiang Zhenxin, Zhou Zongxin
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29 BOOLEAN ALGEBRA BOOLE George Boole (1815 to 1865) was an English mathematician who developed the symbolic analysis of logic now known as Boolean algebra, which is used in the design of digital computers. BOOLEAN ALGEBRA Boolean algebra is the study of operations carried out on variables that can have only two values: 1 (true) or 0 (false). Boolean algebra was developed by George Boole in the 1850s; it is an important part of the theory of logic and has become of tremendous importance since the development of computers.
CENTROID The centroid is the center of mass of an object. It is the point where the object would balance if supported by a single support. For a triangle, the centroid is the point where the three medians intersect. For a onedimensional object of length L, the centroid can be found by using the integral CHAIN RULE 40 L ͐0 xrdx L ͐0 rdx where (x) represents the mass per unit length of the object at a particular location x. The centroid for two- or three-dimensional objects can be found with double or triple integrals.
For example, cos(x) ϭ sin(p/2 Ϫ x). COLLINEAR A set of points is collinear if they all lie on the same line. ) COMBINATIONS The term combinations refers to the number of possible ways of arranging objects chosen from a total sample of size n if you don’t care about the order in which the objects are arranged. ], which is written as n n! j! or else as nCj . ) For example, the number of possible poker hands is equal to the number of possible combinations of five objects drawn (without replacement) from a sample of 52 cards.