Search results
Results from the WOW.Com Content Network
The block-stacking problem is the following puzzle: Place identical rigid rectangular blocks in a stable stack on a table edge in such a way as to maximize the overhang. Paterson et al. (2007) provide a long list of references on this problem going back to mechanics texts from the middle of the 19th century.
As of March 2020, no example of a perfect cuboid had been found and no one has proven that none exist. [5] Euler brick with edges a, b, c and face diagonals d, e, f. Exhaustive computer searches show that, if a perfect cuboid exists, the odd edge must be greater than 2.5 × 10 13, [6] the smallest edge must be greater than 5 × 10 11, [6] and
Famous examples include the number of ways to place n non-attacking rooks on: an entire n × n chessboard, which is an elementary combinatorial problem; the same board with its diagonal squares forbidden; this is the derangement or "hat-check" problem (this is a particular case of the problème des rencontres);
A-C are axis oriented - parallel to axes of the light blue "floor" and also examples of. [1] E shows a maximal empty rectangle with arbitrary orientation In computational geometry , the largest empty rectangle problem, [ 2 ] maximal empty rectangle problem [ 3 ] or maximum empty rectangle problem , [ 4 ] is the problem of finding a rectangle of ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. [1] [2]Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines, which break it up, or partition it, into a collection of smaller matrices.
For example, it is possible to pack 147 rectangles of size (137,95) in a rectangle of size (1600,1230). Packing different rectangles in a rectangle : The problem of packing multiple rectangles of varying widths and heights in an enclosing rectangle of minimum area (but with no boundaries on the enclosing rectangle's width or height) has an ...
The decision problem of whether such a packing exists is NP-hard. This can be proved by a reduction from 3-partition . Given an instance of 3-partition with 3 m positive integers: a 1 , ..., a 3 m , with a total sum of m T , we construct 3 m small rectangles, all with a width of 1, such that the length of rectangle i is a i + m .