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A grid is drawn up, and each cell is split diagonally. The two multiplicands of the product to be calculated are written along the top and right side of the lattice, respectively, with one digit per column across the top for the first multiplicand (the number written left to right), and one digit per row down the right side for the second multiplicand (the number written top-down).
Lattice, or sieve, multiplication is algorithmically equivalent to long multiplication. It requires the preparation of a lattice (a grid drawn on paper) which guides the calculation and separates all the multiplications from the additions. It was introduced to Europe in 1202 in Fibonacci's Liber Abaci. Fibonacci described the operation as ...
Although the original problem asks for integer lattice points in a circle, there is no reason not to consider other shapes, for example conics; indeed Dirichlet's divisor problem is the equivalent problem where the circle is replaced by the rectangular hyperbola. [3]
The grid method (also known as the box method) of multiplication is an introductory approach to multi-digit multiplication calculations that involve numbers larger than ten. Because it is often taught in mathematics education at the level of primary school or elementary school , this algorithm is sometimes called the grammar school method.
Lattice reduction in two dimensions: the black vectors are the given basis for the lattice (represented by blue dots), the red vectors are the reduced basis. In mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different ...
The method for general multiplication is a method to achieve multiplications with low space complexity, i.e. as few temporary results as possible to be kept in memory. . This is achieved by noting that the final digit is completely determined by multiplying the last digit of the multiplic
The hexagonal packing of circles on a 2-dimensional Euclidean plane. These problems are mathematically distinct from the ideas in the circle packing theorem.The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere.
Russian inventor Genrich Altshuller developed an elaborate set of methods for problem solving known as TRIZ, which in many aspects reproduces or parallels Pólya's work. How to Solve it by Computer is a computer science book by R. G. Dromey. [29] It was inspired by Pólya's work.