I have a question that asks if you have a circle with a set amount of points on it you can create some interesting shapes and patterns. It says for example, a circle with 8 points equally placed on it connected to points three point places away creates a star shape. what happens when you change the amount of point spaces and the amounts of points on the circle - ivestigate problems like these. I have got data about how many intersections and how many regions these different circles contain and what types of polygons are formed.
Can someone please assist me with developing an equation or making a conjecture about why certain shapes are formed when different amounts of points and point spaces are used. i.e 6 points connected to other points by 2 point spaces creates 2 overlappin squares..