Here's something mildly interesting and - for me at least - puzzling:
The background is that I have numerous plastic tubes from some plastic shelves I broke down for moving house and have not yet reassembled. These tubes make a good test surface for binding knots, as they are smooth and slippery.
Particularly I have been using them for experimenting with the Gleipnir.
Now, seven tubes make a good bundle, with one in the middle surrounded by six, as seen in pic Tubes01.
On a whim, I drew out the middle tube and was mildly surprised that the structure didn't collapse (Pic Tubes02).
Reflecting on this, I decided that since the middle tube had enforced ideal contact points for each of the surrounding tubes, they were pushing each other apart while the two Gleipnirs pushed them together.
(The string Gleipnir is there to keep the bundle together as I tie and re-tie the braided cord Gleipnir).
So, I've removed about 14% of the volume held by the string, but a gap remains because of a precarious arrangement of compression/tension. OK, but if I disturb that, it will collapse and the bindings will go slack.
Nope. All that happened was that the six tubes could be rearranged into various configurations without ever losing the tension on the bindings. For instance, three over three (Tubes03) or a pyramid of three + two + one (Tubes04).
What the heck is going on? How can I remove 14% of a bound volume without any reduction in the length of line to bind that volume?
