Generation of optimal packings from optimal packings.
Using Baire categories uniqueness of geodesic segments and existence of closed geodesics on typical convex surfaces are investigated.
A classification of dihedral folding tessellations of the sphere whose prototiles are a kite and an equilateral or isosceles triangle was obtained in recent four papers by Avelino and Santos (2012, 2013, 2014 and 2015). In this paper we extend this classification, presenting all dihedral folding tessellations of the sphere by kites and scalene triangles in which the shorter side of the kite is equal to the longest side of the triangle. Within two possible cases of adjacency, only one will be addressed....
We solve problems of Buffon type for a lattice with elementary tile a nonconvex polygon, using as test bodies a line sigment and a circle.
We investigate in a geometrical way the point sets of obtained by the -numeration that are the -integers where is a Perron number. We show that there exist two canonical cut-and-project schemes associated with the -numeration, allowing to lift up the -integers to some points of the lattice ( degree of ) lying about the dominant eigenspace of the companion matrix of . When is in particular a Pisot number, this framework gives another proof of the fact that is...
Die diskrete Ungleichung von W. Wirtinger wird aus den Eigenschaften der auf den mehrdimensionalen Raumen liegenden Polygone gefolgert.