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Pascaline (also known as the arithmetic machine or Pascal's calculator) is a mechanical calculator invented by Blaise Pascal in 1642. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as the supervisor of taxes in Rouen , France. [ 2 ]
PascalABC.NET was developed by a group of enthusiasts at the Institute of Mathematics, Mechanics, and Computer Science in Rostov-on-Don, Russia. [1] In 2003, a predecessor of the modern PascalABC.NET, called Pascal ABC, was implemented by associate professor Stanislav Mikhalkovich to be used for teaching schoolchildren instead of Turbo Pascal, which became outdated and incompatible with modern ...
The Pascal distribution (after Blaise Pascal) and Polya distribution (for George Pólya) are special cases of the negative binomial distribution. A convention among engineers, climatologists, and others is to use "negative binomial" or "Pascal" for the case of an integer-valued stopping-time parameter ( r {\displaystyle r} ) and use "Polya" for ...
Singmaster's conjecture is a conjecture in combinatorial number theory, named after the British mathematician David Singmaster who proposed it in 1971. It says that there is a finite upper bound on the multiplicities of entries in Pascal's triangle (other than the number 1, which appears infinitely many times).
In mathematics, Pascal's pyramid is a three-dimensional arrangement of the trinomial numbers, which are the coefficients of the trinomial expansion and the trinomial distribution. [1] Pascal's pyramid is the three-dimensional analog of the two-dimensional Pascal's triangle , which contains the binomial numbers and relates to the binomial ...
In matrix theory and combinatorics, a Pascal matrix is a matrix (possibly infinite) containing the binomial coefficients as its elements. It is thus an encoding of Pascal's triangle in matrix form. There are three natural ways to achieve this: as a lower-triangular matrix , an upper-triangular matrix , or a symmetric matrix .
The algorithm has already been explained to a large extent, but there are further optimizations. The new presented method [4] gets along with only 5 arithmetic operations per step (for 8 pixels) and is thus best suitable for low-performate systems.
The idea to combine the bisection method with the secant method goes back to Dekker (1969).. Suppose that we want to solve the equation f(x) = 0.As with the bisection method, we need to initialize Dekker's method with two points, say a 0 and b 0, such that f(a 0) and f(b 0) have opposite signs.