Knot

What is Knot?

The term “knot” refers to several distinct concepts depending on the context:

• Cording: A knot is the interlacement of one or more ropes or pliable materials used to bind objects together. The governing principle is that strain draws the parts together, creating friction that allows the knot to hold. Common types include the overhand knot, square knot, bowline, and clove hitch.¹
• Navigation: A knot is a unit of speed used at sea, equivalent to one nautical mile per hour (approximately 1.15 statute miles per hour). The term originated from the knots tied at intervals in a ship’s log line to measure speed.²
• Mathematics: Knot theory is the study of closed curves in three-dimensional space. It examines whether a curve is truly knotted or can be deformed into a simple circle, and whether two curves represent the same knot.³

How do mathematicians use knot theory to study DNA?

Mathematicians apply knot theory to the study of DNA because the molecule often exists as a closed, circular loop that can become physically knotted or supercoiled within a cell. By modeling these structures as closed curves in three-dimensional space, researchers can classify the complexity of DNA configurations and determine whether specific knots can be untangled or transformed into simpler forms.¹⁴

A critical biological application involves the study of topoisomerases, a class of enzymes that regulate the physical state of DNA. These enzymes manage the topological state of the molecule by breaking and rejoining DNA strands to reduce supercoiling or resolve knots that occur during essential processes like replication and recombination. Knot theory provides the mathematical framework to analyze how these enzymes alter the “crossing number” and overall geometry of the DNA molecule, helping scientists understand how cells maintain the structural integrity of their genetic material.⁵⁶¹⁴

What is the difference between a knot, a hitch, and a bend?

In the context of cording and rope work, the terms knot, hitch, and bend refer to specific methods of interlacing rope, each serving a distinct purpose based on how the rope is applied.³

• Knot: In a narrow sense, a knot is a knob or lump formed by turning a rope in on itself, often used to prevent a rope from slipping through an opening or to create a stopper. More broadly, it is the general term for any interlacement of one or more ropes used to bind objects together.³
• Hitch: A hitch is specifically used to attach a rope to another object, such as a spar, post, ring, or hook. These are typically used to secure a line temporarily to an object.³⁷
• Bend: A bend is used to fasten or join one rope to another rope.³

The fundamental principle shared by all three is that the strain applied to the rope draws its constituent parts together, creating friction that allows the configuration to hold.³

Why is the nautical mile defined by the Earth’s circumference?

The nautical mile is defined by the Earth’s circumference because it represents the length of one minute of arc along a meridian of longitude. Since a circle—such as a cross-section of the Earth—contains 360 degrees, and each degree is divided into 60 minutes, the nautical mile provides a practical, standardized unit for navigation based on the planet’s geometry.¹⁰

Historically, as sea voyages extended further from land in the 15th century, sailors required a reliable way to measure distance without visible landmarks. By linking distance to the Earth’s angular measurements, navigators could determine their position more accurately. While the Earth is an oblate spheroid rather than a perfect sphere—meaning the actual length of a minute of arc varies slightly by latitude—an international standard of 1,852 meters was adopted in 1929 to provide a consistent global measurement.¹⁰