Théorème de Cauchy (géométrie)En géométrie, le théorème de Cauchy, ou théorème de rigidité de Cauchy, affirme que tout polyèdre convexe est rigide. Autrement dit, si les faces de deux polyèdres convexes sont deux à deux isométriques, ces polyèdres sont isométriques. Un patron de polyèdre convexe détermine le polyèdre initial de façon unique. Ce résultat est fondamental pour la théorie de la rigidité : une conséquence en est qu'un modèle physique d'un polyèdre convexe obtenu en reliant des faces rigides par des charnières flexibles est indéformable.
Arrangement of linesIn geometry, an arrangement of lines is the subdivision of the plane formed by a collection of lines. Problems of counting the features of arrangements have been studied in discrete geometry, and computational geometers have found algorithms for the efficient construction of arrangements. Intuitively, any finite set of lines in the plane cuts the plane into two-dimensional polygons (cells), one-dimensional line segments or rays, and zero-dimensional crossing points.
Arrangement of hyperplanesIn geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains when the hyperplanes are removed from the whole space. One may ask how these properties are related to the arrangement and its intersection semilattice.
Discrete calculusDiscrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. The word calculus is a Latin word, meaning originally "small pebble"; as such pebbles were used for calculation, the meaning of the word has evolved and today usually means a method of computation. Meanwhile, calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the study of continuous change.
Incidence (geometry)In geometry, an incidence relation is a heterogeneous relation that captures the idea being expressed when phrases such as "a point lies on a line" or "a line is contained in a plane" are used. The most basic incidence relation is that between a point, P, and a line, l, sometimes denoted P I l. If P I l the pair (P, l) is called a flag. There are many expressions used in common language to describe incidence (for example, a line passes through a point, a point lies in a plane, etc.
Conjecture de Keplervignette|250x250px|Empilement compact de 35 sphères. La conjecture de Kepler est une ancienne conjecture (démontrée en 1998 et certifiée en 2014) formulée par le physicien, astronome et mathématicien Johannes Kepler en 1611. Cette conjecture énonce que, pour un empilement de sphères égales, en espace libre, la densité maximale est atteinte pour un empilement compact de plans compacts. Cette densité d vaut environ 74 % : vignette|250x250px|empilement de trois plans compacts de sphères: succession A,B,C ou succession A,B,A.
