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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 ...

The triangle line that passes through the inner and outer Soddy centers S and S^'. The Soddy line is central line L_(657) and has trilinear equation ...

Given two intersecting lines OA and OB forming an angle with vertex at O and a point X inside the angle ∠AOB, the Philo line (or Philon line) is the shortest line segment AB ...

Using disk point picking, x = sqrt(r)costheta (1) y = sqrt(r)sintheta (2) for r in [0,1], theta in [0,2pi), choose two points at random in a unit disk and find the ...

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 ...

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

The nine-point center N (sometimes instead denoted F) is the center of the nine-point circle. It has equivalent triangle center functions alpha_5 = cos(B-C) (1) alpha_5 = ...

The prime distance pd(n) of a nonnegative integer n is the absolute difference between n and the nearest prime. It is therefore true that pd(p)=0 for primes p. The first few ...

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...