What is infinite knots?

Infinite knots, also known as endless knots, are a type of mathematical knot that do not have a distinct beginning or end. They are formed by continuously looping a single strand of rope or string so that it intersects with itself in a pattern that is repeatable to infinity.

Unlike other types of knots, infinite knots are not commonly used in practical applications, such as tying shoelaces or securing cargo. Instead, they are primarily used in the field of topology, which is the study of geometric properties that are unchanged by continuous transformations.

Infinite knots can come in a variety of forms and sizes, ranging from simple patterns like the trefoil knot to more complex structures like the Borromean rings. They are often used to illustrate mathematical concepts or as decorative motifs in art and jewelry.

One interesting property of infinite knots is that they can be classified based on their behavior when cut into two pieces. Some knots will remain as one piece after being cut, while others will split into multiple disconnected parts. This property is known as knot complements, and it is a key concept in the study of knot theory.