Search Results for ""

A point, such as interior points of a disk, such that (px)(py)=[const], where p is the chord length.

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 ...

Given a unit line segment [0,1], pick two points at random on it. Call the first point x_1 and the second point x_2. Find the distribution of distances d between points. The ...

A disk with radius 1. The (open) unit disk can also be considered to be the region in the complex plane defined by {z:|z|<1}, where |z| denotes the complex modulus. (The ...

A Jensen disk is a disk in the complex plane whose diameter joins complex conjugate roots of a polynomial (Trott 2004, p. 22).

Select three points at random on the circumference of a unit circle and find the distribution of areas of the resulting triangles determined by these three points. The first ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

The unit lower half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]<0}.

The unit upper half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]>0}.

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...