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Abacus. An abacus ( pl.: abaci or abacuses ), also called a counting frame, is a hand -operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Arabic numeral system. [1] An abacus consists of a two-dimensional array of slidable beads (or similar objects).
Halley's method. In numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name. The algorithm is second in the class of Householder's methods, after Newton's ...
Meantone temperament. Meantone temperaments are musical temperaments, that is a variety of tuning systems, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them narrower than a perfect fifth ), in order to push the thirds closer to pure. Meantone temperaments are constructed similarly to Pythagorean tuning ...
t. e. The frequency response plot from Butterworth's 1930 paper. [1] The Butterworth filter is a type of signal processing filter designed to have a frequency response that is as flat as possible in the passband. It is also referred to as a maximally flat magnitude filter.
Padé approximant. In mathematics, a Padé approximant is the "best" approximation of a function near a specific point by a rational function of given order. Under this technique, the approximant's power series agrees with the power series of the function it is approximating. The technique was developed around 1890 by Henri Padé, but goes back ...
This picture shows clockwise from top left: An Arithmometer, a Comptometer, a Dalton adding machine, a Sundstrand, and an Odhner Arithmometer. A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically, or (historically) a simulation such as an analog computer or a ...
Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity.
The Legendre polynomials were first introduced in 1782 by Adrien-Marie Legendre [3] as the coefficients in the expansion of the Newtonian potential. where r and r′ are the lengths of the vectors x and x′ respectively and γ is the angle between those two vectors. The series converges when r > r′.