Bights & Columns

One of the most familiar ways to describe a knot is by its bights. Bights correlate to a knot’s diameter or width - a 3-bight knot is much narrower than an 8-bight knot.

The labels seen here can be toggled at Options > Canvas & Image: Show Pin Labels.

Cylindrical Knots

For cylindrical knots like Turks Head or Pineapple, bights is the number of turning points in the top bight ring labeled A.

This Turks Head knot has 9 bights labeled A1 to A9.

Mat Knots

For mat knots, bights is the number of bights in the top row plus 1. This is because there is an implied half-bight in each corner that only becomes visible when the knot is open-ended.

Notice how this closed-loop knot has 9 bights along both the top and bottom rows. Here we look at the top row and add 1, which means this knot has 10 bights.

Notice how this nearly identical open-ended knot has 9 bights in the top row and 10 bights in the bottom row. Again, we look at the top row and add 1, which means this knot has 10 bights.

In this image, Options > Canvas & Image: Show Grid Boundary is toggled on. The ghost column exists to accommodate open-ended strands. It’s needed to offset the bottom bights from the top bights, and to account for the half-bight tails at each end.

Nested Knots

A bight nest is a mirrored pair of top and bottom bight rings. A Turks Head has 1 bight nest - one pair of top-bottom bight rings. Knots like the Pineapple typically have 1 bight nest per strand, color, or pass.

For example, this knot is 3 equally sized and interwoven Turks Heads. It has 3 bight nests - 3 pairs of top and bottom rings.

The 3 Turks Heads are tied on the AD, BE, and CF ring pairs. However, the topological mirrored pairs are actually AF, BE, and CD.

Stated another way, the mirrored pairs in bight nests are about pin placement - and not about which pairs a strand must occupy. This is an interesting aspect of knot theory that’s cool to know - the important thing is understanding this knot has 5 bights and 3 bight nests.

Total Bights & Columns

Total Bights is the number of bights in the top half of the knot.

• For knots like the Turks Head that have only 1 bight nest, total bights is the number of bights in the A ring.
• For mat knots, recall there is a ‘ghost’ column. Total bights is the number of bights in the top row plus 1.
• For nested knots, total bights is the number of bights times bight nests.

The mathematical relationship between bights and grid columns is: Columns = Total Bights * 2. This knot has:

• 4 bights (A1 to A4)
• 3 bight nests (rings ABC)
• 12 total bights (4B x 3BN)
• 24 columns (12 * 2)