Knotted bands vs. Circular knots, part one

In light of the popularity of circular Celtic knots, today I am going to run a little experiment. I want to see what relationship exists between the length of a knot and its circular counterpart.

Below are four open-ended Celtic knots of one, two, three, and four segments, along with a circular Celtic knot of the same number of segments.

1-4 segment knots
1-4 segment knots

Below are four open-ended Celtic knots of five, six, seven, and eight segments along with a circular Celtic knot of the same number segments.

5-8 segment knots
5-8 segment knots

Below are four open-ended Celtic knots of nine, ten, eleven, and twelve segments along with a circular Celtic knot of the same number of segments.

9-12 segment knots
9-12 segment knots

Now looking at these twelve examples, I come to three conclusions:

  1. Circular knots with odd-number segments make one continuous knot;
  2. Circular knots with even-number segments make two interlocking knots;
  3. The more segments, the “bumpier” the inner and outer edges of the circular knot.

My next experiment will determine the relationship between the depth of a knot and its circular counterpart.

See you tomorrow . . .

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