I decided to dive deeper into the subject of mechanical construction and dividing a straight line into equal segments. The applet shows you how to use a ruler and a compass to divide a line into N segments. I still wasn't happy with this technique because it requires multiple tools and the lines go off the page.
From the mechanical construction technique I noted that a reference line is created of arbitrary length. The line is created by drawing N segments and then projecting this onto the line we are trying to divide. This tutorial uses a similar technique, but using the paper itself as the line segments. You might find this useful, so take a look!
Line up the pages along the long end.
a) Draw two lines from the center point to the bottom corners (marked in green).
b) The red lines drawn from the intersection of the green lines and the meeting page edges indicate the third folds.