square_distance

square_distance, a Python code which computes the expected value of the distance between a pair of points randomly selected inside the unit square in 2D.

Licensing:

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

Languages:

square_distance is available in a MATLAB version and a Python version.

Related Data and Programs:

ball_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the interior of the unit ball in 3D.

circle_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected on the circumference of the unit circle in 2D.

cube_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the interior of the unit cube in 3D.

disk_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the interior of the unit disk in 2D.

hyperball_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the interior of the unit hyperball in M dimensions.

hypersphere_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected on the surface of the unit hypersphere in M dimensions.

line_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected in the unit line segment.

normal01_multivariate_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected from an isotropic standard normal distribution in M dimensions.

sphere_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected on the surface of the unit sphere in 3D.

triangle_distance, a Python code which considers the problem of describing the typical value of the distance between a pair of points randomly selected form the interior of a triangle in 2D.

Reference:

• Paul Nahin,
  Will You Be Alive 10 Years From Now?,
  Princeton, 2014,
  ISBN: 978-0691156804.
• Eric Weisstein,
  Square Line Picking,
  From MathWorld--A Wolfram Web Resource,
  https://mathworld.wolfram.com/SquareLinePicking.html

Source Code:

• square_distance.py, the source code.
• square_distance.sh, runs all the tests.
• square_distance.txt, the output file.

• square_distance_compare.png, compares observed and theoretical values of the PDF.
• square_distance_histogram.png, a histogram of the sample results.
• square_distance_pdf.png, a plot of the theoretical probability density function.