Knot Theory and Topology

The unknot is the simplest knot, as it is a closed curve in 3-space that can be continuously deformed into a circle without passing through itself.

The square knot is the knot that is formed by tying a shoelace in the standard way. It is also known as the reef knot or the granny knot.

The overhand knot is the knot that is formed by tying a rope into a loop and then passing one end of the rope through the loop. It is also known as the simple knot or the thumb knot.

The bowline knot is the knot that is formed by tying two ropes together. It is a strong and secure knot that is often used in sailing and climbing.

The clove hitch is the knot that is formed by tying a rope around an object. It is a simple and secure knot that is often used in camping and hiking.

The double overhand knot is the knot that is formed by tying a rope into a loop and then passing the end of the rope through the loop twice. It is also known as the figure-eight knot.

The triple overhand knot is the knot that is formed by tying a rope into a loop and then passing the end of the rope through the loop three times. It is also known as the granny knot.

The quadruple overhand knot is the knot that is formed by tying a rope into a loop and then passing the end of the rope through the loop four times. It is also known as the square knot.

The quintuple overhand knot is the knot that is formed by tying a rope into a loop and then passing the end of the rope through the loop five times. It is also known as the granny knot.

The sextuple overhand knot is the knot that is formed by tying a rope into a loop and then passing the end of the rope through the loop six times. It is also known as the square knot.

The septuple overhand knot is the knot that is formed by tying a rope into a loop and then passing the end of the rope through the loop seven times. It is also known as the granny knot.

The octuple overhand knot is the knot that is formed by tying a rope into a loop and then passing the end of the rope through the loop eight times. It is also known as the square knot.

The nonuple overhand knot is the knot that is formed by tying a rope into a loop and then passing the end of the rope through the loop nine times. It is also known as the granny knot.

The decuple overhand knot is the knot that is formed by tying a rope into a loop and then passing the end of the rope through the loop ten times. It is also known as the square knot.

The undecuple overhand knot is the knot that is formed by tying a rope into a loop and then passing the end of the rope through the loop eleven times. It is also known as the granny knot.