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Complex exponential function: The exponential function exactly maps all lines not parallel with the real or imaginary axis in the complex plane, to all logarithmic spirals in the complex plane with centre at : () = (+) + ⏟ = + = ( + ) ⏟ The pitch angle of the logarithmic spiral is the angle between the line and the imaginary axis.
Graphs of roses are composed of petals.A petal is the shape formed by the graph of a half-cycle of the sinusoid that specifies the rose. (A cycle is a portion of a sinusoid that is one period T = 2π / k long and consists of a positive half-cycle, the continuous set of points where r ≥ 0 and is T / 2 = π / k long, and a negative half-cycle is the other half where r ...
A path graph (or linear graph) consists of n vertices arranged in a line, so that vertices i and i + 1 are connected by an edge for i = 1, …, n – 1. A starlike tree consists of a central vertex called root and several path graphs attached to it. More formally, a tree is starlike if it has exactly one vertex of degree greater than 2.
Branch decomposition of a grid graph, showing an e-separation.The separation, the decomposition, and the graph all have width three. In graph theory, a branch-decomposition of an undirected graph G is a hierarchical clustering of the edges of G, represented by an unrooted binary tree T with the edges of G as its leaves.
Fermat's spiral: a>0, one branch = + Fermat's spiral, both branches. A Fermat's spiral or parabolic spiral is a plane curve with the property that the area between any two consecutive full turns around the spiral is invariant.
He then moves to opposite side of the crown and locates the point under that branch tip. The spread along that line is the horizontal distance between those two positions. On steeply sloping ground (over 15 degrees) the taped distance between the two points can be corrected to a true horizontal by using basic trigonometry.
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 ...
The planar graph obtained from the blossom tree above. The green lines connect the opening and closing stems. An embedded planar graph can be built from a blossom tree by connecting each opening stem to a closing stem. One visits the half-edges by going around the graph clockwise starting at an opening stem.