mathematical knots

Mathematical knots are loops of string embedded in three-dimensional space that are tangled or intertwined but have no ends, meaning they are closed loops. Unlike everyday knots, the focus is on their intrinsic shape—how they are tangled—rather than how they are tied or tied and untied. Mathematicians study these knots to understand their properties, classify different types of knots, and explore how they can be transformed into one another without cutting. This field, called knot theory, has applications in biology, chemistry, and physics, helping to analyze DNA, molecules, and the nature of space itself.