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..
Okay, well the question is an investigation and you have to draw circles with a varying amount of points on them and then connect these points by a set number of point spaces..
for example, a circle with six point connected every one point space, a circle with 6 points connected ever 2 point spaces, a circle with six points connected every 3 points spaces and so on... then you draw some more circles with a different amount of points i,e 5 points. 8 points etc and do the same to these.. for example a circle with six points connected every 2 point spaces gives you 2 overlapping triangles, a circle with six points connected every 3 point spaces gives a 'bicycle wheel' shape etc..
Is there any formula to calculate how many points of intersection a circle with a set amount of points will have?
Is there a formula to calculate the maximum amount of regions a circle can have with a set number of points... i.e what is the maximum number of regions a circle with 8 points can have when the points can be connected by point spaces? The maximum number of regions always occurs for even numbers when the number of point spaces used is half the amount of points on the circle take one. But this does not work for odd numberss