Drawing stars is a fun activity. Once you learn how, you can make some really cool looking stars with any number of points you want.

Also, drawing stars can be related to a number of mathematical concepts, such as:

multiples and factoring

prime numbers

symmetry

geometry terms (polygon, vertex, edge)

Vi Hart has a great video about drawing stars. She goes pretty quickly, so I’ve included instructions below.

A star polygon is a figure formed by connecting every qth point out of p regularly spaced points lying on a circle. The star polygon is denoted by {p,q}. So for example, the 5-pointed star, that we are all familiar with, is a {5,2} star, because it has 5 points (p), and you make it by connecting every 2nd (qth) point.

To create the star polygon:

Start with a circle.

Decide how many points you want your star to have, and place that number of equally spaced dots around that circle.

Choose a starting point.

Draw a line to the point q spaces over.

Repeat until you are back to a starting point.

If you reach a starting point and not all points have been covered, lift the pencil, skip over 1 point, and repeat the process. As shown for the {6,2} star below:

I have a worksheet, with these instructions and pre-printed circles and points, available here.

So, how do these cool stars relate to all those other math concepts?

Stars where you can touch all points without lifting your pencil, such as the {5,2} star, are called regular polygon stars. In these cases, p and q are relatively prime, which means they have no common factors. Another example is the {10,3} star. There are no numbers (besides 1) that divide evenly into both 10 and 3.

{10,3}

In cases that create “asterick” stars (such as {8,4}) or regular polygon stars (the ones where you had to lift your pencil), q is a divisor of p. Or you can say the p is a multiple of q. The {9,3} star consists of 3 regular triangles.

{8,4}

{9,3}

The number of lines of symmetry for a star polygon is equal to the number of vertices (points).