Suppose you have a triangular lattice, and you are tracing out a polygonal closed curve, show that if the internal angles are more than 60 then there must be a point on the lattice in the interior of the curve.
This problem came up when I was trying to solve this problem:from James Tanton Which could be easily solved by pick’s theorem and in fact a converse of this could be used to prove my question, however I was looking for a simpler approach more similar to a Pestov-Ionin theorem for polygonal curves
