![]() ![]() ![]() Ogni volta che fai scoppiare una bolla, si ridurrà di dimensioni ma verrà. In questo gioco, il tuo obiettivo è sparare alle bolle con il diavolo Usa la tua pistola a punta per far scoppiare tutte le bolle dalle parti più grandi a quelle più piccole. In a fascinating postscript, a group of four undergraduates doing research last summer under Morgan's direction managed to extend the double bubble result to four dimensions, and, with some extra conditions, to five and higher dimensions as well. Bubble Trouble è un gioco sparabolle arcade creato da Kresimir Cvitanovic. Their proof rests on arguments about rotations and stability. In order to be sure that the genuine and only minimal surface was the familiar double bubble, the existence of a nonstandard minimizer had to be definitively ruled out - and that is what a team of fourįrank Morgan of Williams College, Massachusetts, Michael Hutchings of Stanford, and Manuel Ritori and Antonio Ros of Granada proved their result using only pencil and paper, despite the fact that the earlier proof (in 1995) of the special case when both volumes are the same was computer-aided, and very long. Here the larger region is broken into two components, one a tiny ring, like a torus,Īround the other region, which is also torus-like.Īlthough noone had managed to find a minimal surface among these strange configurations, or "non-standard bubbles", mathematicians need more than this to conclude that none exists. These configurations are never seen in nature, and can only be seen using computer modelling. The trouble was that, although the familiar double bubble configuration certainly satisfied all the known conditions, so did some other, considerably stranger, configurations. For example, the surface would have to be rotationally symmetric about a line, and consist of surfaces meeting in threes at 120 o angles along curves. Some facts about any minimal surface enclosing and separating two volumes have been known for some time, however. But progress on the two-volume problem - "How small can a surface be while enclosing and separating two given volumes?" - has been slower. The minimal surface enclosing a single volume is a sphere, as was asserted by Archimedes and proved by Schwarz in 1884. How small can a surface be while still enclosing and separating some number of given volumes?Ī solution to the last of these problems is known as a minimal surface.How can a task be carried out as quickly as possible?.If the two bubbles enclose the same volume, the separating surface is flat.Ī common theme of many problems in mathematics is that of efficiency. Find the lyrics and meaning of any song, and watch its music video. The three surfaces meet along a circle at 120 o. in trouble I step up in the game and I burst that bubble Uh oh youre in trouble I step up in the game and I burst that bubble Uh oh youre in trouble I step. In a double bubble, the joining surface bulges a little into the larger of the two bubbles. Four mathematicians have finally confirmed that the familiar double soap bubble is indeed the best way to enclose two separate volumes of air. ![]()
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