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Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics .
The definition of an atlas depends on the notion of a chart. A chart for a topological space M is a homeomorphism from an open subset U of M to an open subset of a Euclidean space. The chart is traditionally recorded as the ordered pair (,). [1]
Acrobat Reader Touch is a free PDF document viewer developed and released on December 11, 2012, by Adobe Systems for the Windows Touch user interface. FormsCentral was a web form filling server for users with Windows, macOS, or a web browser and an Adobe ID only.
In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon , using "sept-" (an elision of septua- , a Latin -derived numerical prefix , rather than hepta- , a Greek -derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning angle.
The girth of an undirected graph can be computed by running a breadth-first search from each node, with complexity () where is the number of vertices of the graph and is the number of edges. [7] A practical optimization is to limit the depth of the BFS to a depth that depends on the length of the smallest cycle discovered so far. [ 8 ]
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection. [1] The metric connection is a specialization of the affine connection to surfaces or other manifolds endowed with a metric, allowing distances to be measured on that surface.
Geometric graph theory in the broader sense is a large and amorphous subfield of graph theory, concerned with graphs defined by geometric means. In a stricter sense, geometric graph theory studies combinatorial and geometric properties of geometric graphs, meaning graphs drawn in the Euclidean plane with possibly intersecting straight-line edges, and topological graphs, where the edges are ...