Mathematics: Kepler’s problem for eight-dimensional balls

Once encrypted the astronomer Johannes Kepler as you must stack balls to make as many as possible in a box. Now, a mathematician will have solved the problem for eight-dimensional balls.

How do you layer balls so that the space is used optimally? More than 400 years ago, the astronomer Johannes Kepler formulated a guess to do so. The evidence was however only in 1998 – and only by using a computer.

Everyone knows the densest sphere packing from the supermarket: when oranges to great pyramids are stacked, they intuitively just like by Kepler proposed. In the first position, touching Orange form three regular triangles. The oranges of the next layer are placed in the gaps of the layer underneath.
This layering fills the space to 74.5 percent. A pyramid of oranges is therefore nearly three quarters of Orange and slightly more than a quarter of air.

The sphere packing problem, there are not only in the three-dimensional space, but also for higher dimensions. We can imagine that no four – or five-dimensional ball – physicist as mathematician but easily calculate in higher-dimensional spaces.

Maryna Viazovska, a post-doctorate at the Berlin Mathematical School, wants to now have solved the packing problem for eight-dimensional balls. According to their work, the space can be fill with balls then up to 25.4 percent.
Viazovskas proof is however as yet not officially recognized. The mathematician has published him has only been on the platform, on which researchers upload work, even if they still traverse the examination procedure of journals (Peer Review).