Yesterday night i think i proved the following theorem:
theorem
among all the possible regular polygons inscribed in a given circle, the hexagon is the only one with a side length equal to the circle radius.
First of all, i invite every one to prove or disprove and to teach me if i did a mistake.
It was easy, it is an elementary statement, so i think that someone already found it, my first question is: where i can find some references about this result and others in the same field?
Actually the theorem told us that given six equal length sticks, we can always build an hexagon, and so my second question: is because of this that hexagons are common in nature?