Knotted bands vs. Circular knots, part two

Did you like yesterday’s experiment? I used a simple, single-thickness, open-ended knot segment, and showed how increasing the number of segments affected the circular Celtic knot (the knotted band just got longer).

Today, I will increase the thickness of the open-ended knot sequence.

Below are examples of a two-layer open ended knot sequence using one through eight segments, both as knotted bands then as a circular knot.

1-8 segment 2-layer knots
1-8 segment 2-layer knots

Below are examples of a three-layer open ended knot sequence using one through eight segments, both as knotted bands then as a circular knot.

1-8 segment 3-layer knots
1-8 segment 3-layer knots

Below are examples of a four-layer open ended knot sequence using one through eight segments, both as knotted bands then as a circular knot.

1-8 segment 4-layer knots
1-8 segment 4-layer knots

From these examples, I draw the following conclusions:

  1. The thickness of the knotted bands increases with each new layer;
  2. The thickness of the circular knots remains the same with each new layer;
  3. The thickness of the circular knots will never reach the center of the circle, regardless of the number of layers;
  4. As more segments are added, the “woven-ness” of the knot is better defined;
  5. As more layers are added, the thinner the woven strands.

I did not trace the circular knots to determine if they are single- or multiple-strand knots based on the number of segments (perhaps you’d care to give it a try??).

The circular knots in these experiments have been unbroken, and continuous. My next experiment will introduce breaks along the outer and inner edges.

See you tomorrow . . .

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