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The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + ... and so forth for the 64 squares. The total number of grains can be shown to be 2 64 −1 or 18,446,744,073,709,551,615 (eighteen quintillion ...
Multiplication algorithm. A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the topic. The oldest and simplest method, known since antiquity as long ...
Mathematics of paper folding. Map folding for a 2×2 grid of squares: there are eight different ways to fold such a map along its creases. The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability (whether the model can be flattened ...
Marching squares. In computer graphics, marching squares is an algorithm that generates contours for a two-dimensional scalar field (rectangular array of individual numerical values). A similar method can be used to contour 2D triangle meshes . The contours can be of two kinds:
(There are several ways to pick these patterns—those distinguish between the various superimposed codes; we discuss them below). When a new book comes in, make a new card for it: Get a blank card with the standard N holes in it and write down the name of the book, etc. in the middle. Write down the subjects covered by the book on the card.
v. t. e. Weighted least squares ( WLS ), also known as weighted linear regression, [ 1][ 2] is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations ( heteroscedasticity) is incorporated into the regression. WLS is also a specialization of generalized least squares, when all ...
A Graeco-Latin square or Euler square or pair of orthogonal Latin squares of order n over two sets S and T (which may be the same), each consisting of n symbols, is an n × n arrangement of cells, each cell containing an ordered pair (s, t), where s is in S and t is in T, such that every row and every column contains each element of S and each element of T exactly once, and that no two cells ...
One can consider a Latin square as a complete bipartite graph in which the rows are vertices of one part, the columns are vertices of the other part, each cell is an edge (between its row and its column), and the symbols are colors. The rules of the Latin squares imply that this is a proper edge coloring.
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