Virtual Knot Theory extends classical knot theory by incorporating virtual crossings alongside traditional over‐ and under‐crossings. Originating from Kauffman’s work in the late 20th century, the ...

Researchers have analyzed the mechanical forces underpinning simple knots, and come up with a theory that describes how a knot's topology determines its mechanical forces. Got rope? Then try this ...

This is a preview. Log in through your library . Abstract Any 2-dimensional knot K can be presented in a braid form, and its braid index, Braid(K), is defined. For the connected sum K₁#K₂ of 2-knots ...

You may not have heard of knot theory. But take it from Bill Menasco, a knot theorist of 35 years: This field of mathematics, rich in aesthetic beauty and intellectual challenges, has come a long way ...

Sometimes, a simple, even childish question turns out to be connected to the deepest secrets of the universe. Here’s one: How many different ways can you tie your shoelaces? Mathematicians have been ...

Quandle theory has emerged as a vital algebraic framework for understanding knots and links, capturing the underlying symmetries that distinguish one knot from another. At its essence, a quandle is an ...

Braiding—the interlacing of three or more strands—seems fairly straightforward, but as any parent of a long-haired child will tell you, it takes skilled hands to master the technique. Braiding a ...