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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 following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.
A transition map provides a way of comparing two charts of an atlas. To make this comparison, we consider the composition of one chart with the inverse of the other. This composition is not well-defined unless we restrict both charts to the intersection of their domains of definition. (For example, if we have a chart of Europe and a chart of ...
An example of a chart containing gratuitous chartjunk. This chart uses a large area and much "ink" (many symbols and lines) to show only five hard-to-read numbers, 1, 2, 4, 8, and 16. Chartjunk consists of all visual elements in charts and graphs that are not necessary to comprehend the information represented on the graph, or that distract the ...
The web graph W 4,2 is a cube. The web graph W n,r is a graph consisting of r concentric copies of the cycle graph C n, with corresponding vertices connected by "spokes". Thus W n,1 is the same graph as C n, and W n,2 is a prism. A web graph has also been defined as a prism graph Y n+1, 3, with the edges of the outer cycle removed. [7] [10]
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Kramer reported that grade 12 IMP students in his study performed better on all areas of mathematics tested by the NAEP test, [13] and Webb and Dowling reported IMP students performed significantly better on statistics questions from the Second International Mathematics Study, on mathematical reasoning and problem solving tasks designed by the ...
The crown graph can be viewed as a complete bipartite graph from which the edges of a perfect matching have been removed, as the bipartite double cover of a complete graph, as the tensor product K n × K 2, as the complement of the Cartesian direct product of K n and K 2, or as a bipartite Kneser graph H n,1 representing the 1-item and (n – 1 ...
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