Let $\vec x$ be a random unit vector (that is, a random vector on the unit sphere). Let $x_i$ be the $i$'th coordinate (if it is easier, you can assume we are in 3-dimensional space). What is the distribution of $|x_i|$? More specifically, what is…
I am not sure if this question makes sense or is even ideal, but here is my problem: Many proposed distance formulas only give a distance in terms of 1-dimensions. A common distance formula is the Euclidean distance (the most obvious one). Euclidean…
Suppose I have N points (labeled 1, 2, ..., k, ..., N) in D dimensions. I'd like to choose the order of points such that, after each point, the volume of the convex hull is maximized.
In other words, the volume of the convex hull is a function of…
