figure-eight knot
figure-of-eight knot

The figure-eight knot has played an important role historically (and continues to do so) in the theory of 3-manifolds.

A loose figure-eight knot is tied in the end of one rope.

He quickly tied a figure-eight knot in one end of the forty-five-foot line.

A lightly tightened figure-eight knot is formed around the standing part of the line such that both ends emerge from the same point.

The only other hyperbolic knot with 7 or more is the figure-eight knot, which has 10.

It is more bulky and less prone to jamming than the closely related figure-eight knot.

Baby Fuzzy looked up disinterestedly, and then went back to trying to untie a figure-eight knot he had tied.

However, it is not currently known whether the figure-eight knot is the only one that achieves the bound of 10.

The figure-eight knot is a type of knot.

From this perspective, the figure-eight knot can be considered the simplest hyperbolic knot.

For example, the Gieseking manifold is commensurate to the complement of the figure-eight knot.

The trefoil knot has genus one, as does the figure-eight knot.

The figure-eight knot, with four crossings, is the simplest non-torus knot.

The symmetry between and in the Jones polynomial reflects the fact that the figure-eight knot is achiral.

The result is two figure-eight knots, each partly inside the other and tightening its hold on the other when they are pulled in opposite directions.

This knot can replace the figure-eight knot when tying into a climbing harness.

The figure-eight knot is prime, alternating, rational with an associated value of 5/2, and is achiral.

When used outside of heraldry (as a real knot), it is known as a figure-eight knot.

The trefoil knot and figure-eight knot are not Lissajous.

The figure-eight knot is not tricolorable.

Figure-eight knot as a stopper.

By way of example, the unknot has crossing number zero, the trefoil knot three and the figure-eight knot four.

There are two loops at the front of the harness where the climber ties into the rope at the working end using a figure-eight knot.

One can easily make a loop using a double figure eight knot by doubling the rope, then tying the standard figure-eight knot.

It has long been known that most of the simple knots, such as the trefoil knot and the figure-eight knot are invertible.

Because of the way the knots are tied, the digit 1 cannot be shown this way and is represented in this position by a figure-of-eight knot.

Although it is a stable knot, it is often backed up with a stopper knot, such as a figure-of-eight knot, for safety.

For example, if 4s represents four simple knots, 3L represents a long knot with three turns, E represents a figure-of-eight knot and X represents a space:

Realising if he hooked back the curtain it would let in a little light from the corridor, he tied the cumbersome velvet into a huge figure-of-eight knot, then turned back to face whatever lay ahead.

Their work may represent the first identification of a quipu element for a non-numeric concept, a sequence of three figure-of-eight knots at the start of a quipu that seems to be a unique signifier.

The knot is formed by following the steps to make a figure-of-eight knot, but the working end makes an additional wrap around the standing part before passing back through the initial loop in the same direction it would have for a figure-of-eight knot.