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Many of the puzzles of this type involve packing rectangles or polyominoes into a larger rectangle or other square-like shape. There are significant theorems on tiling rectangles (and cuboids) in rectangles (cuboids) with no gaps or overlaps: An a × b rectangle can be packed with 1 × n strips if and only if n divides a or n divides b. [15] [16]
Sphere packing finds practical application in the stacking of cannonballs. In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three- dimensional Euclidean space. However, sphere packing problems can be ...
A cuboid is a hexahedron with quadrilateral faces, meaning it is a polyhedron with six faces. It has eight vertices and twelve edges. Etymologically, "cuboid" means "like a cube ", in the sense of a convex solid which can be transformed into a cube by adjusting the lengths of its edges and the angles between its adjacent faces.
An almost-perfect cuboid has 6 out of the 7 lengths as rational. Such cuboids can be sorted into three types, called body, edge, and face cuboids. [13] In the case of the body cuboid, the body (space) diagonal g is irrational. For the edge cuboid, one of the edges a, b, c is irrational. The face cuboid has one of the face diagonals d, e, f ...
The bin packing problem[1][2][3][4] is an optimization problem, in which items of different sizes must be packed into a finite number of bins or containers, each of a fixed given capacity, in a way that minimizes the number of bins used. The problem has many applications, such as filling up containers, loading trucks with weight capacity ...
Recycling trash can in Natal, Brazil. A waste container, also known as a dustbin, [1] rubbish bin, trash can, and garbage can, among other names, is a type of container intended to store waste that is usually made out of metal or plastic. The words "rubbish", "basket" and "bin" are more common in British English usage; "trash" and "can" are ...
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The cube is a special case among every cuboids. As mentioned above, the cube can be represented as the rectangular cuboid with edges equal in length and all of its faces are all squares. [ 1 ] The cube may be considered as the parallelepiped in which all of its edges are equal edges.