I was hanging lights on a Christmas tree yesterday, and thought of a problem , which may have an easy solution - but not one that I can think of off the top of my head. It is posed as follows: Consider hanging lights on a Christmas tree. A light strand has a light bulb every $k$ cm, and the Christmas tree is a cone with height $h$ and radius $r$. Is there a way to wrap the lights around the tree such that the lights have a uniform distribution on the surface area of the cone.
More precisely, is there a method which works for all cones, by which one can draw a continuous line on the surface of a cone in such a way that points every $k$ apart on the line form a uniform distribution on the surface of the cone.
Is there a simple solution? Or is it much more complicated than it seems?