# python_distance

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.

### Related Data and Programs:

annulus_distance, a Python code which estimates the typical distance between a pair of points randomly selected in a circular annulus in 2D.

ball_distance, a Python code which estimates the typical distance between a pair of points randomly selected in the unit ball in 3D.

circle_distance, estimates the typical distance between a pair of points randomly selected on the circumference of the unit circle in 2D.

cube_distance, a Python code which estimates the typical distance between a pair of points randomly selected in the unit cube in 3D.

cube_surface_distance, a Python code which estimates the typical distance between a pair of points randomly selected on the surface of the unit cube.

disk_distance, a Python code which estimates the typical distance between a pair of points randomly selected in the unit disk in 2D.

ellipse_distance, a Python code which estimates the typical distance between a pair of points randomly selected on the perimeter of an ellipse (x/a)^2+(y/b)^2=1.

hyperball_distance, a Python code which estimates the typical distance between a pair of points randomly selected in the unit hyperball in M dimensions.

hypercube_distance, a Python code which estimates the typical distance between a pair of points randomly selected in the M-dimensional unit hypercube.

hypercube_surface_distance, a Python code which estimates the typical distance between a pair of points randomly selected on the surface of the unit hypercube in D dimensions.

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.

hypersphere_distance, a Python code which estimates the typical distance betweena pair of points randomly selected on the unit hypersphere in M dimensions.

levenshtein_distance, a Python code which returns the Levenshtein distance between two strings.

line_distance, a Python code which estimates the typical distance betweena pair of points randomly selected in the unit line segment in 1D.

normal01_multivariate_distance, a Python code which estimates the typical distance betweena pair of points randomly selected from an isotropic standard normal distribution in M dimensions.

permutation_distance, a Python code which estimates the expected value of the Ulam distance between a pair of randomly selected permutations of the same order.

polygon_distance, a Python code which estimates the typical distance betweena pair of points randomly selected from a polygon in 2D.

sphere_distance, a Python code which estimates the typical distance betweena pair of points randomly selected on the surface of the unit sphere in 3D.

square_distance, a Python code which estimates the typical distance betweena pair of points randomly selected in the unit square in 2D.

square_surface_distance, a Python code which estimates the typical distance between a pair of points randomly selected on the surface of the unit square.

subset_distance, a Python code which estimates the expected value of the Hamming distance between a pair of randomly selected subsets of an M set.

triangle_distance, a Python code which estimates the typical distance between a pair of points randomly selected in a triangle in 2D.

Last revised on 07 December 2022.