**hypersphere_angle_distance**,
a Python 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. In dimension 1, we have average dot product
of 1, and angle 0. As the dimension increases, the average dot product
rapidly decreases to 0, while the average angle goes to 90 degrees.

The computer code and data files made available on this web page are distributed under the MIT license

**hypersphere_angle_distance** is available in
a MATLAB version and
an Octave version and
a Python version.

hypersphere, a Python 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.

python_distance, a Python code which estimates the typical distance between a pair of points randomly selected from the surface or interior of a geometric object such as a circle, disk, sphere, cube.

- hypersphere_angle_distance.py, the source code.
- hypersphere_angle_distance.sh, runs all the tests.
- hypersphere_angle_distance.txt, the output file.