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Line chart. A line chart or line graph, also known as curve chart, [ 1] is a type of chart that displays information as a series of data points called 'markers' connected by straight line segments. [ 2] It is a basic type of chart common in many fields. It is similar to a scatter plot except that the measurement points are ordered (typically by ...
The top left graph is linear in the X and Y axes, and the Y-axis ranges from 0 to 10. A base-10 log scale is used for the Y axis of the bottom left graph, and the Y axis ranges from 0.1 to 1,000. The top right graph uses a log-10 scale for just the X axis, and the bottom right graph uses a log-10 scale for both the X axis and the Y axis.
The Riemann zeta function ζ(s) is a function of a complex variable s = σ + it, where σ and t are real numbers. (The notation s, σ, and t is used traditionally in the study of the zeta function, following Riemann.) When Re (s) = σ > 1, the function can be written as a converging summation or as an integral: where. is the gamma function.
In a line graph L(G), each vertex of degree k in the original graph G creates k(k − 1)/2 edges in the line graph. For many types of analysis this means high-degree nodes in G are over-represented in the line graph L(G). For instance, consider a random walk on the vertices of the original graph G.
It is known that ζ(3) is irrational (Apéry's theorem) and that infinitely many of the numbers ζ(2n + 1) : n ∈ , are irrational. [1] There are also results on the irrationality of values of the Riemann zeta function at the elements of certain subsets of the positive odd integers; for example, at least one of ζ (5), ζ (7), ζ (9), or ζ ...
The graph of the logarithm base 2 crosses the x-axis at x = 1 and passes through the points (2, 1), (4, 2), and (8, 3), depicting, e.g., log 2 (8) = 3 and 2 3 = 8. The graph gets arbitrarily close to the y-axis, but does not meet it. Addition, multiplication, and exponentiation are three of the most fundamental arithmetic operations.
In graph theory, a line perfect graph is a graph whose line graph is a perfect graph. Equivalently, these are the graphs in which every odd-length simple cycle is a triangle. [1] A graph is line perfect if and only if each of its biconnected components is a bipartite graph, the complete graph K4, or a triangular book K1,1,n. [2]
Pareto chart. A Pareto chart is a type of chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line. The chart is named for the Pareto principle, which, in turn, derives its name from Vilfredo Pareto, a noted Italian economist.