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Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects ... unit volume polyhedra of a given ... For example, it ...
Water pouring puzzles (also called water jug problems, decanting problems, [1] [2] measuring puzzles, or Die Hard with a Vengeance puzzles) are a class of puzzle involving a finite collection of water jugs of known integer capacities (in terms of a liquid measure such as liters or gallons). Initially each jug contains a known integer volume of ...
Reprint of 1935 edition. A problem on page 101 describes the shape formed by a sphere with a cylinder removed as a "napkin ring" and asks for a proof that the volume is the same as that of a sphere with diameter equal to the length of the hole. Pólya, George (1990), Mathematics and Plausible Reasoning, Vol.
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.
Some SI units of volume to scale and approximate corresponding mass of water. To ease calculations, a unit of volume is equal to the volume occupied by a unit cube (with a side length of one). Because the volume occupies three dimensions, if the metre (m) is chosen as a unit of length, the corresponding unit of volume is the cubic metre (m 3).
Doubling the cube, also known as the Delian problem, is an ancient [a] [1]: 9 geometric problem. Given the edge of a cube , the problem requires the construction of the edge of a second cube whose volume is double that of the first.
Each volume the contains problems at the beginning and (brief) solutions at the end. As two authors have put it, "there is a general consensus among mathematicians that the two-volume Pólya-Szegő is the best written and most useful problem book in the history of mathematics." [1]: 59
The third of Hilbert's list of mathematical problems, presented in 1900, was the first to be solved. The problem is related to the following question: given any two polyhedra of equal volume, is it always possible to cut the first