Star Polygons Page 4 of 5

Suppose n is an integer greater than 2 and d is either 1 or n-1. What type of figure is Star(n,d)? (I already know it's a star polygon, so be more specific.)

Sketch the following pairs of star polygons.

Star(8,3) and Star(8,5)

Star(12,5) and Star(12,7)

Star(15,7) and Star(15,8)

Make a conjecture about the relationship between Star(n,s) and Star(n,r) when the sum of s and r is n. Be sure that your entire conjecture fits in the box shown below.

Recall that Star(n,d) is a star polygon or a star figure depending on whether n and d have any common factors. A star polygon can always be drawn with a single continuous path, whereas a star figure always requires more than one path. How many continuous paths are required to complete each star?

Star(8,2)

Star(13,5)

Star(16,4)

Star(12,9)

When you are satisfied with your results, print this page and continue with the next.