Mathematicians have found a way to simultaneously contact 7 cylinders

More than 50 years ago, Martin Gardner, the author of the popular articles on mathematics in the journal American American, proposed the following task to readers: “Can you place seven cigarettes in such a way that each of them comes into contact with everyone else?”

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

Half a century later - on March 20, 2014 - at the Gathering 4 Gardner conference in honor of Gardner, the mathematician from the Hungarian Academy of Sciences Sandor Bozoki (Sándor Bozóki) announced the appropriate decision. Last summer it was published in a scientific article on ArXiv.
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To search for a successful configuration, Bozoki and colleagues spent three months of computer time. They constituted a system of polynomial equations describing the position of the generator cylinders in three-dimensional space.

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



Both results were checked using AlphaCertified to prove that the solutions found were not the result of any computer rounding errors. Scientists even made a real physical model of wood. However, in the production of wooden parts, the error is even greater than rounding errors in computer calculations can be, so this model is made solely for demonstration purposes.