hypersphere_angle, an Octave code which considers the problem of describing the typical value of the angle between a pair of points randomly selected on the unit hypersphere in M dimensions. Since by symmetry, this will be zero, we instead look at the average of the absolute value of the dot product, and the corresponding angle. This starts out at 1 for dimension 1, and rapidly decreases as the spatial dimension increases.
The information on this web page is distributed under the MIT license.
hypersphere_angle is available in a MATLAB version and an Octave version and a Python version.
hypersphere, an Octave code which carries out various operations for an M-dimensional hypersphere, including converting between Cartesian and spherical coordinates, stereographic projection, sampling the surface of the sphere, and computing the surface area and volume.
hypersphere_distance, an Octave code which considers the problem of describing the typical value of the distance between a pair of points randomly selected on the unit hypersphere in M dimensions.