19 Jul '08 18:531 edit

Suppose I mark a circle of a particular radius, and then mark out along its edge a number of equally spaced dots. Connecting these dots in one manner would result in a regular polygon.

Suppose then I were to count the number of distinct ways of connecting all the dots with one continuous set of straight lines, ending with the dot I started with, with rotations and mirror images being considered identical.

With 3 dots, I have one way of connecting the dots

With 4 dots, I have two ways of connecting the dots

With 5 dots, I have 4 ways of connecting the dots

Remember, the dots are evenly spaced about a normal circle, and I have to connect the dots without "lifting the pen" so to speak, so patterns like a Star of David won't work, as that requires 2 sets of lines.

Suppose then I were to count the number of distinct ways of connecting all the dots with one continuous set of straight lines, ending with the dot I started with, with rotations and mirror images being considered identical.

With 3 dots, I have one way of connecting the dots

*(triangle)*With 4 dots, I have two ways of connecting the dots

*(square or hourglass)*With 5 dots, I have 4 ways of connecting the dots

*(pentagon, star, "fish", or a "wave"-type pattern)***How many distinct ways can you connect 6 dots?**Remember, the dots are evenly spaced about a normal circle, and I have to connect the dots without "lifting the pen" so to speak, so patterns like a Star of David won't work, as that requires 2 sets of lines.