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Dessins D'enfants
In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann surfaces and to provide combinatorial Invariant (mathematics), invariants for the action of the absolute Galois group of the rational numbers. The name of these embeddings is French language, French for a "child's drawing"; its plural is either ''dessins d'enfant'', "child's drawings", or ''dessins d'enfants'', "children's drawings". A dessin d'enfant is a undirected graph, graph, with its vertex (graph theory), vertices colored alternately black and white, graph embedding, embedded in an Orientability, oriented surface that, in many cases, is simply a Plane (mathematics), plane. For the coloring to exist, the graph must be bipartite graph, bipartite. The faces of the embedding are required be topological disks. The surface and the embedding may be described combinatorially using a rotation system, a cyclic order of the edges surrounding each vertex of the graph that describes the order in which th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
