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Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

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 ...

A complex line bundle is a vector bundle pi:E->M whose fibers pi^(-1)(m) are a copy of C. pi is a holomorphic line bundle if it is a holomorphic map between complex manifolds ...

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 ...