Numeerisen analyysin ja laskennallisen
tieteen seminaari
3.4.2006 klo
14.15
U356
Michal Krizek, Mathematical Institute, Czech Academy of Sciences
There is no
face-to-face partition of R5
into acute
simplices
We prove that a point in the Euclidean space R5 cannot be surrounded by a finite number of acute simplices. This fact implies that there does not exist a face-to-face partition of R5 into acute simplices. The existence of an acute simplicial partition of $R^d$ for $d>5$ is excluded by induction, but for $d=4$ this is an open problem.