On the eve of the Olympic Games, we are closing the first season of mathematical puzzles on the open problem of squaring the cube. It involved cutting a hollow cube into several pieces in order to reconstruct a square. In particular, I suggested trying to achieve this division with as few pieces as possible.
There were twenty-two of you who participated and offered me a total of thirty-four different cuts. Two of you discovered four-piece cuts! The one in figure A was discovered by Jérôme Petitjean and the one presented in figure B by Jérôme Roche. These two figures start from the same cube pattern before cutting it into four pieces.
However, reading all your solutions, I thought it was a shame to publish the proposals with only the minimum number of parts, because you could imagine a particularly surprising diversity of methods. Figure C, for example, shows a solution designed by Rault Stanislas and using the cut of Vesa Timonen’s mitre that I presented to you in the puzzle. By cutting the six faces of the cube in two diagonally, it is possible to easily reconstruct a mitre in which it will be enough to reproduce the cut discovered by Timonen at the beginning of the year. Doing mathematics often means knowing how to return to a problem you already know!
Since I have limited space in this section, you can find a full review of the solutions I received on the site. World.
Please note, however, that to date there is no evidence that we cannot do better. If you manage to find a solution in less than four parts, or if you have proof that this is not possible, please write to the email address laquadratureducube@micmaths.fr. I will be sure to keep you informed about the future progress of the problem.
All this still leaves me some room to pose a short riddle for you next week. If we write the numbers in letters and order them alphabetically, “zero” will obviously be the last one. But which number will be the first? And the second? The third?
Find previous puzzles by clicking here
