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Ebook Dictionary of mathematics terms (3rd edition): Part 2

The book "Dictionary of mathematics terms" also lists and defines mathematical symbols, includes a brief table of integrals, and describes how to derive key theorems. Filled with illustrative diagrams and equations. | 203 MANDELBROT SET M MACLAURIN Colin Maclaurin (1698 to 1746) was a Scottish mathematician who extended the field of calculus. (See Maclaurin series.) MACLAURIN SERIES The Maclaurin series is a special case of the Taylor series for f (x ϩ h), when x ϭ 0. (See Taylor series.) MAGNITUDE The magnitude of a vector a is its length. It is symbolized by two pairs of vertical lines, and it can be found by taking the square root of the dot product of the vector with itself: ʈaʈ ϭ 2a # a For example, the magnitude of the vector (3, 4) is 213,42 # 13,42 ϭ 29 ϩ 16 ϭ 225 ϭ 5 MAJOR ARC A major arc of a circle is an arc with a measure greater than 180°. (See arc.) MAJOR AXIS The major axis of an ellipse is the line segment joining two points on the ellipse that passes through the two foci. It is the longest possible distance across the ellipse. (See ellipse.) MAJOR PREMISE The major premise is the sentence in a syllogism that asserts a general relationship between classes of objects. (See syllogism.) MANDELBROT SET The Mandelbrot set, discovered by Benoit Mandelbrot, is a famous fractal, i.e., a shape containing an infinite amount of fine detail. It is the set of values of c for which the series znϩ1 ϭ z2 ϩ c converges, n MANTISSA 204 Figure 76 Mandelbrot set where z and c are complex numbers and z is initially (0,0). (See complex number.) Figure 76 shows the whole set and an enlargement of a small area. On the plot, x and y are the real and imaginary parts of c. The Mandelbrot set is the black bulbous object in the middle; elsewhere, the stripes indicate the number of iterations needed to make 0z 0 exceed 2. MANTISSA The mantissa is the part of a common logarithm to the right of the decimal point. For example, in the expression log 115 ϭ 2.0607, the quantity 0.0607 is the mantissa. For contrast, see characteristic. MAPPING A mapping is a rule that, to each member of one set, assigns a unique member of another set. MATHEMATICAL INDUCTION Mathematical induction is a method .