Length of fishing thread

A liitle bit weaving technique is given here. This is important especially when one want to weave a long strip of beads (or equivalently zigzag carbon nanoribbon, ZGNR) with a width that consists of one or two hexagons, or more generally, odd or even numbers of hexagons. When we want to make a Mobius ZGNR, we will meet the situation like this. Basically, we need to weave a long strip first and then connect both ends in a particular way.

If we want to weave a long strip of ZGNR with a width of one hexagon, corresponding to a polyacene, we should observe that the length of fishing threads in both hands are running out at equal rate. It is easy to understand this by checking the following figure (a).

However, if we want to weave ZGNR with a width of two hexagons as shown in the bottom of the following figure (b), we should easily see that the one end of thread runs out much faster than the other end. It is also easy to understand why that happen by looking at the figure.

Of course, one can avoid this problem by following different weaving path. (see (c) of the following figure) I usually don't like to use weaving path (c). This is because weaving path (c) has the problem that it is much harder to make the structure constructed by this path tight.