Search results
Results from the WOW.Com Content Network
Maximum disjoint set (or Maximum independent set) is a problem in which both the sizes and the locations of the input rectangles are fixed, and the goal is to select a largest sum of non-overlapping rectangles. In contrast, in rectangle packing (as in real-life packing problems) the sizes of the rectangles are given, but their locations are ...
Packing identical rectangles in a rectangle: The problem of packing multiple instances of a single rectangle of size (l,w), allowing for 90° rotation, in a bigger rectangle of size (L,W) has some applications such as loading of boxes on pallets and, specifically, woodpulp stowage. For example, it is possible to pack 147 rectangles of size (137 ...
A root-phi rectangle divides into a pair of Kepler triangles (right triangles with edge lengths in geometric progression). The root-φ rectangle is a dynamic rectangle but not a root rectangle. Its diagonal equals φ times the length of the shorter side. If a root-φ rectangle is divided by a diagonal, the result is two congruent Kepler triangles.
Problems of this type included finding the dimensions of a rectangle given its area and the amount by which the length exceeds the width. Tables of values of n 3 + n 2 were used to solve certain cubic equations. For example, consider the equation: + =. Multiplying the equation by a 2 and dividing by b 3 gives:
Of particular interest to rectilinear polygons are problems of decomposing a given rectilinear polygon to simple units - usually rectangles or squares. There are several types of decomposition problems: In covering problems, the goal is to find a smallest set of units (squares or rectangles) whose union is equal to the polygon. The units may ...
A cushion filled with stuffing. In geometry, the paper bag problem or teabag problem is to calculate the maximum possible inflated volume of an initially flat sealed rectangular bag which has the same shape as a cushion or pillow, made out of two pieces of material which can bend but not stretch.
The area thus obtained is referred to as the sofa constant. The exact value of the sofa constant is an open problem. The leading solution, by Joseph L. Gerver, has a value of approximately 2.2195. In November 2024, Jineon Baek posted an arXiv preprint claiming that Gerver's value is optimal, which if true, would solve the moving sofa problem. [2]
In geometry, a golden rectangle is a rectangle with side lengths in golden ratio +:, or :, with approximately equal to 1.618 or 89/55. Golden rectangles exhibit a special form of self-similarity : if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.