## I: Images using Subdivisions

**String Art using Subdivisions between Vertices**

Part I keys off of the notion of creating ** S** equally spaced subdivisions between vertices. The image is created by connecting subdivision points that are

**subdivisions from one another via connected line segments until the starting point is once again attained.**

*P*Given * n* vertices and

*subdivisions between vertices there are a total of*

**S*******

*n***possible endpoints for line segments rather than**

*S**possible endpoints used in the Polygons and Stars file. There are*

**n****subdivisions between points used to create the line segments in each image and the image is created one segment at a time until the initial vertex (top of the polygon) is once again reached and the circuit is completed.**

*P*Completing the circuit need not take * n**

**jumps. For example, let**

*S***= 3 and**

*n***= 2 and consider**

*S***= 1, 2, and 3. When**

*P**= 1, it takes six segments to complete the image with two segments on each side of the equilateral triangle. If*

**P****= 2, the same equilateral triangle is mapped out in three segments. If**

*P**= 3, the image is the vertical line from the top to the midpoint of the base and then back to the top.*

**P**If we consider * P* = 4 and 5 we obtain exactly the same images as

**= 2 and 1, but if you follow the order in which lines are drawn, they**

*P**appear*to be drawn counterclockwise. The same is true whenever

*/2 <*

**n***<*

**P****. In general, the image with**

*n***=**

*P**–*

**n****is a mirror image of the image with**

*j***=**

*P***. Another initial point to note is that if**

*j****

**n****is even, then**

*S***=**

*P******

*n***/2 always produces in image of a vertical line.**

*S*