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In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144 ...
3.3 Slow convergence for roots of multiplicity greater than 1. ... at the values of 1, 10, and −20. Each row in a "x n" column is ... a number smaller than this ...
A query is a request for information from a database. It can be as simple as "find the address of a person with Social Security number 123-45-6789," or more complex like "find the average salary of all the employed married men in California between the ages 30 to 39 who earn less than their spouses." The result of a query is generated by ...
More generally, there are d! possible orders for a given array, one for each permutation of dimensions (with row-major and column-order just 2 special cases), although the lists of stride values are not necessarily permutations of each other, e.g., in the 2-by-3 example above, the strides are (3,1) for row-major and (1,2) for column-major.
In the second line, the number one is added to the fraction, and again Excel displays only 15 figures. In the third line, one is subtracted from the sum using Excel. Because the sum in the second line has only eleven 1's after the decimal, the difference when 1 is subtracted from this displayed value is three 0's followed by a string of eleven 1's.
The second row is the same generator with a seed of 3, which produces a cycle of length 2. Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8]. A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation.
The Z-ordering can be used to efficiently build a quadtree (2D) or octree (3D) for a set of points. [5] [6] The basic idea is to sort the input set according to Z-order.Once sorted, the points can either be stored in a binary search tree and used directly, which is called a linear quadtree, [7] or they can be used to build a pointer based quadtree.
In 1930, Lev Schnirelmann proved that any natural number greater than 1 can be written as the sum of not more than C prime numbers, where C is an effectively computable constant; see Schnirelmann density. [13] [14] Schnirelmann's constant is the lowest number C with this property. Schnirelmann himself obtained C < 800 000.