Let's name each set of more than three points "connectable", when it is possible to connect all of the points that belong to set with n line segments (where n is number of points) in such a way that they create a n-gon that don't intersect itself. Of course, points are placed in two dimensional space.
Here are two examples of connectable sets(Sorry for bad quality of the pictures):
Next example shows points connected in improper way, the created polygon have only six sides, while the set consists of seven points(The orange point lies on the straight line segment).
This set, and the previous one are not connectable.
My question is: Can we easily determine whether given set is connectable or not?
For example the set below looks like if it wasn't connectable, but I didn't managed to prove this.
Thanks for all the help.
from Hot Weekly Questions - Mathematics Stack Exchange
Post a Comment