Mathematicians have found a way to simultaneously contact 7 cylinders

More than 50 years ago, the author of popular articles about mathematics in Scientific American, Martin Gardner offered readers a challenge: "Can you accommodate seven cigarettes so that each of them is in contact with all the others?»

Gardner himself has found a solution, but it did not satisfy him, because some of the base cylinder in contact with the side surfaces. He wanted a solution in which the base of the cylinder would not be used. That is the case with an infinitely long cylinder.

Half a century later - March 20, 2014 - Conference on Gathering 4 Gardner after Gardner, a mathematician at the Hungarian Academy of Sciences Bozok Sándor (Sándor Bozóki) announced yet suitable solution. Last summer it was published in a scientific article on ArXiv.

To search for a good configuration Bozok colleagues spent three months of computer time. They amounted to a system of polynomial equations describing the position forms a cylinder in three-dimensional space.

Number of possible configurations was estimated at about 121 billion, and check all of them was not possible. But scientists are lucky: after checking 80 million configurations were found two solutions.



Both results are checked using AlphaCertified, to prove that the solutions - not the result of some kind of computer rounding errors. Scientists have even produced a real physical model of the tree. However, in the manufacture of wooden parts even more errors than can be rounding errors in computer calculations, so that this model is made solely for demonstration purposes.

Source: habrahabr.ru/post/218403/