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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) = ...

The intersection of an ellipse centered at the origin and semiaxes of lengths a and b oriented along the Cartesian axes with a line passing through the origin and point ...

The plane determined by the points x_1, x_2, and x_3 and the line passing through the points x_4 and x_5 intersect in a point which can be determined by solving the four ...

The negative pedal curve of a line specified parametrically by x = at (1) y = 0 (2) is given by x_n = 2at-x (3) y_n = ((x-at)^2)/y, (4) which is a parabola.

A curve in two dimensions on which the value of a function f(x,y) is a constant. Other synonymous terms are isarithm, isopleth, and contour line. A plot of several ...

A Pareto plot is type of plot used in quality control applications that combines a bar chart displaying percentages of categories in the data with a line graph showing ...

Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...