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The graph is said to be circularly embedded onto the manifold, in that every face of the embedding is a simple cycle in the graph. However, a cycle double cover of a graph with degree greater than three may not correspond to an embedding on a manifold: the cell complex formed by the cycles of the cover may have non-manifold topology at its ...
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...
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 1000. 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 cube and regular octahedron are dual graphs of each other. According to Steinitz's theorem, every polyhedral graph (the graph formed by the vertices and edges of a three-dimensional convex polyhedron) must be planar and 3-vertex-connected, and every 3-vertex-connected planar graph comes from a convex polyhedron in this way.
For instance, the double cover of K 4 is the graph of a cube; the double cover of the Petersen graph is the Desargues graph; and the double cover of the graph of the dodecahedron is a 40-vertex symmetric cubic graph. [3] It is possible for two different graphs to have isomorphic bipartite double covers.
Visual demonstration of the double-angle formula for sine. For the above isosceles triangle with unit sides and angle 2 θ {\displaystyle 2\theta } , the area 1 / 2 × base × height is calculated in two orientations.
A double exponential function (red curve) compared to a single exponential function (blue curve). A double exponential function is a constant raised to the power of an exponential function . The general formula is f ( x ) = a b x = a ( b x ) {\displaystyle f(x)=a^{b^{x}}=a^{(b^{x})}} (where a >1 and b >1), which grows much more quickly than an ...
In this case, if + + is not 0 then the curve has a point of double contact with =. If the coefficient of x 2 , c 0 + 2 m c 1 + c 2 m 2 , {\displaystyle c_{0}+2mc_{1}+c_{2}m^{2},} is 0 but the coefficient of x 3 is not then the origin is a point of inflection of the curve.