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A graph G is said to be locally X, where X is a graph (or class of graphs), when for every vertex v, the graph induced on G by the set of adjacent vertices of V (sometimes ...

Sphere line picking is the selection of pairs of points corresponding to vertices of a line segment with endpoints on the surface of a sphere. n random line segments can be ...

Consider a line segment of length 1, and pick a point x at random between [0,1]. This point x divides the line into line segments of length x and 1-x. If a set of points are ...

In the figure above with tangent line PT and secant line PA, (PA)/(PT)=(PT)/(PB) (1) (Jurgensen et al. 1963, p. 346). The line tangent to a circle of radius a centered at ...

The mean line segment length l^_ is the average length of a line segment in line segment picking within some given shape. As summarized in the following table (where Delta(3) ...

The equation of a line ax+by+c=0 in slope-intercept form is given by y=-a/bx-c/b, (1) so the line has slope -a/b. Now consider the distance from a point (x_0,y_0) to the ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

A number of points on a line segment. The term was first used by Desargues (Cremona 1960, p. x). If the points A, B, C, ... lie on a line segment with the coordinates of the ...

Given a regular tetrahedron of unit volume, consider the lengths of line segments connecting pairs of points picked at random inside the tetrahedron. The distribution of ...

The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...