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The solution in which the three rectangles are all of different sizes and where they have aspect ratio ρ 2, where ρ is the plastic ratio. The fact that a rectangle of aspect ratio ρ 2 can be used for dissections of a square into similar rectangles is equivalent to an algebraic property of the number ρ 2 related to the Routh–Hurwitz ...
The fair polygon partitioning problem [20] is to partition a (convex) polygon into (convex) pieces with an equal perimeter and equal area (this is a special case of fair cake-cutting). Any convex polygon can be easily cut into any number n of convex pieces with an area of exactly 1/n. However, ensuring that the pieces have both equal area and ...
Divide and choose (also Cut and choose or I cut, you choose) is a procedure for fair division of a continuous resource, such as a cake, between two parties. It involves a heterogeneous good or resource ("the cake") and two partners who have different preferences over parts of the cake (both want as much of it as possible).
Recycling codes on products. Recycling codes are used to identify the materials out of which the item is made, to facilitate easier recycling process.The presence on an item of a recycling code, a chasing arrows logo, or a resin code, is not an automatic indicator that a material is recyclable; it is an explanation of what the item is made of.
In a proportional cake-cutting, each person receives a piece that he values as at least 1/n of the value of the entire cake. In the example cake, a proportional division can be achieved by giving all the vanilla and 4/9 of the chocolate to George (for a value of 6.66), and the other 5/9 of the chocolate to Alice (for a value of 5). In symbols:
It was found that the most effective version was strips of black paper backed with aluminium foil, exactly 27 cm × 2 cm (10.63 in × 0.79 in) and packed into bundles each weighing 1 pound (0.45 kg). The head of the TRE, A. P. Rowe , code-named the device "Window".
The maximum number of pieces from consecutive cuts are the numbers in the Lazy Caterer's Sequence. When a circle is cut n times to produce the maximum number of pieces, represented as p = f (n), the n th cut must be considered; the number of pieces before the last cut is f (n − 1), while the number of pieces added by the last cut is n.
The precise origins of the dimensions of US letter-size paper (8.5 × 11 in) are not known. The American Forest & Paper Association says that the standard US dimensions have their origin in the days of manual papermaking, the 11-inch length of the standard paper being about a quarter of "the average maximum stretch of an experienced vatman's arms". [2]