On Convex Bodies that Permit Packings of High Density.
On coverings with convex domains
On geodesics of phyllotaxis
Seeds of sunflowers are often modelled by leading to a roughly uniform repartition with seeds indexed by consecutive integers at angular distance for the golden ratio. We associate to such a map a geodesic path of the modular curve and use it for local descriptions of the image of the phyllotactic map .
On Gnomons
On packing of squares into a rectangle
On parametric density of finite circle packings.
On seven points in the boundary of a plane convex body in large relative distances.
On some packings of the hyperbolic plane by incongruent hypercyclic domains.
On the area discrepancy of triangulations of squares and trapezoids.
On the cover time of planar graphs.
On the Hadwiger numbers of centrally symmetric starlike disks.
On the lower bound of packing density for convex bodies in the plane.
On the perimeter of the intersection of congruent disks.
On the thinnest 2-fold double-lattice covering with a centrally symmetric convex domain. (Über die dünnste doppelgitterförmige 2-fache Überdeckung mit einem zentralsymmetrischen konvexen Bereich.)
On-line Covering the Unit Square with Squares
The unit square can be on-line covered with any sequence of squares whose total area is not smaller than 4.
On-line Packing Squares into n Unit Squares
If n ≥ 3, then any sequence of squares of side lengths not greater than 1 whose total area does not exceed ¼(n+1) can be on-line packed into n unit squares.
Optimal packings for filled rings of circles
General circle packings are arrangements of circles on a given surface such that no two circles overlap except at tangent points. In this paper, we examine the optimal arrangement of circles centered on concentric annuli, in what we term rings. Our motivation for this is two-fold: first, certain industrial applications of circle packing naturally allow for filled rings of circles; second, any packing of circles within a circle admits a ring structure if one allows for irregular spacing of circles...
Optimisation hybride par colonies de fourmis pour le problème de découpe à deux dimensions
Nous nous intéressons dans cet article au problème de découpe guillotine en deux dimensions noté 2BP/O/G. Il s'agit de découper un certain nombre de pièces rectangulaires dans un ensemble de plaques de matière première, elles même rectangulaires et identiques. Celles-ci sont disponibles en quantité illimitée. L'objectif est de minimiser le nombre de plaques utilisées pour satisfaire la demande, en appliquant une succession de coupes, dites guillotines, allant de bout en bout. Nous proposons une approche...
Packing 10 or 11 unit squares in a square.
Packing and covering a unit equilateral triangle with equilateral triangles.