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An arrangement in which the midpoint of all the spheres lie on a single straight line is called a sausage packing, as the convex hull has a sausage-like shape.An approximate example in real life is the packing of tennis balls in a tube, though the ends must be rounded for the tube to coincide with the actual convex hull.
Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, people are given:
Under STP, a reaction between three cubic meters of hydrogen gas and one cubic meter of nitrogen gas will produce about two cubic meters of ammonia.. The law of combining volumes states that when gases chemically react together, they do so in amounts by volume which bear small whole-number ratios (the volumes calculated at the same temperature and pressure).
The Reeve tetrahedra in three dimensions have four integer points as vertices and contain no other integer points, but do not all have the same volume. Therefore, there does not exist an analogue of Pick's theorem in three dimensions that expresses the volume of a polyhedron as a function only of its numbers of interior and boundary points. [20]
The law was named after scientist Jacques Charles, who formulated the original law in his unpublished work from the 1780s.. In two of a series of four essays presented between 2 and 30 October 1801, [2] John Dalton demonstrated by experiment that all the gases and vapours that he studied expanded by the same amount between two fixed points of temperature.
Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship. If volume increases, then pressure decreases and vice versa, when the temperature is held constant. Therefore, when the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved.
Image credits: anon #5. When I was in medschool I was tangentially friends with a guy who never showed up to uni at all. Skipped all lectures, called in sick for all lab and tutorial sessions.
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 ...