#average distance

Finding the average distance in a polygon

Finding the average distance in a polygon Over the previous couple of posts I’ve looked at the average distance in squares, rectangles and equilateral triangles.  The logical extension to this is to consider a regular polygon with sides 1.   Above is pictured a regular pentagon with sides 1 enclosed in a 2 by 2 square.  The points N and O represent 2 randomly chosen points which we find the…

Finding the average distance in an equilateral triangle

Finding the average distance in an equilateral triangle In the previous post I looked at the average distance between 2 points in a rectangle.  In this post I will investigate the average distance between 2 randomly chosen points in an equilateral triangle. Drawing a sketch. The first step is to start with an equilateral triangle with sides 1.  This is shown above.  I sketched this using Geogebra…

Finding the average distance between 2 points on a hypercube

Finding the average distance between 2 points on a hypercube This is the natural extension from this previous post which looked at the average distance of 2 randomly chosen points in a square – this time let’s explore the average distance in n dimensions.  I’m going to investigate what dimensional hypercube is required to have an average distance of more than one, and then also what happens to…