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Gauss's continued fraction. In complex analysis, Gauss's continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first analytic continued fractions known to mathematics, and it can be used to represent several important elementary functions, as well as some of the more complicated ...
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 2 , − 8 5 , −8 5 , and 8 −5 .
Starting at 0, add 1 for each cell whose distance to the origin (0,0) is less than or equal to r. When finished, divide the sum, representing the area of a circle of radius r, by r2 to find the approximation of π. For example, if r is 5, then the cells considered are: (−5,5) (−4,5)
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
The lowest common denominator of a set of fractions is the lowest number that is a multiple of all the denominators: their lowest common multiple. The product of the denominators is always a common denominator, as in: but it is not always the lowest common denominator, as in: Here, 36 is the least common multiple of 12 and 18.
But every number, including π, can be represented by an infinite series of nested fractions, called a continued fraction: = + + + + + + + + Truncating the continued fraction at any point yields a rational approximation for π ; the first four of these are 3 , 22 / 7 , 333 / 106 , and 355 / 113 .
A difference engine is an automatic mechanical calculator designed to tabulate polynomial functions. It was designed in the 1820s, and was first created by Charles Babbage . The name difference engine is derived from the method of divided differences , a way to interpolate or tabulate functions by using a small set of polynomial co-efficients.
V.P.A.M. is similar to the Direct Algebraic Logic (D.A.L.) used by Sharp in some of their scientific calculators. The fx-82ES introduced by Casio in 2004 was the first calculator to incorporate the Natural Textbook Display (or Natural Display) system. It allowed the display of expressions of fractions, exponents, logarithms, powers and square ...