Why you don't get to choose the zig length

The drawing program always scales zigzags so that they fit neatly into the display area. Different choices of zig angle and zag angle can give zigzags of greatly differing sizes: for example, if the angles are very small (say 1 degree), then the zigzag will extend a long way to the right before it begins to turn around and move to the left again. In fact, a good estimate of the horizontal and vertical dimensions of the zigzag (measured in the same units as the zigs and zags themselves) is
ê
ê
ê 		100
sin(q1/2)
 ê
ê
ê 		+ ê
ê
ê 		l2
sin(q2/2)
 ê
ê
ê 		,
where q1 and q2 are the zig and zag angles respectively, and l2 is the zag length (the zig length l1 belongs in the numerator of the first fraction, but is fixed at 100). You can see that if either q1 or q2 is very close to 0 (or to 360), then the value on the bottoms of the corresponding fraction will be very small (why?) and so the dimension will be very large.

Since the drawing program always scales the zigzags, choosing the zig length to be 100 and the zag length to be 200 would give exactly the same result as choosing the zig length to be 35 and the zag length to be 70: namely, a zigzag in which the zags are twice as long as the zigs. In other words, what matters isn't the zig and zag lengths themselves, but the ratio between them. Thus we can fix the zig length to be 100, and choose the zag length to give the right ratio between zigs and zags.

In fact, you can't quite do everything this way. Suppose you wanted the zigs to be exactly three times as long as the zags: since the zag length has to be a whole number, you can make it either 33 or 34, but not 33 and a third. However, since small changes in the zag length make very little difference to the zigzag, this is the sort of inaccuracy that we can live with.

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