A polytope P of 3-space, which meets a given lattice L only in its vertices, is called L-elementary. An L-elementary tetrahedron has volume ≥ (1/6). det(L), in case equality holds it is called L-primitive. A result of Knudsen, Mumford and Waterman, tells us that any convex polytope P admits a linear simplicial subdivision into tetrahedra which are primitive with respect to the bigger lattice (1/2) t .L, for some t depending on P . Improving this, we show that in fact the lattice (1/4).L always suffices. To this end, we first characterize all L-elementary tetrahedra for which even the intermediate lattice (1/2).L suffices.
A Tale of Bridges: Topology and Architecture Topology, as its name indicates, is a (mathematical) way of conceiving of TOPOS: the place, the space, all space, and everything included in it. JeanMichel Kantor evokes a few examples of forms and spaces which should be stimulating for all those interested in the concept of space, architects in particular. In topology, we no longer distinguish between two figures, two spaces, if you can pass from one to the other by means of a continuous deformation -with neither leap nor cut. Knots are a simple way of escaping from the obtuseness of space. Modern techniques of visualization developed for the military or for the Hollywood studios of Lucas Films can integrate the deformations on computer screens: the continued deformations of surfaces are discretized, that is, they are replaced by approximations produced at fixed intervals, then filmed in video. The time of the virtual corresponds to the era of topology, and architects are finding inspiration there.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.