Knot theory

Uncommon card · No. 108576

In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, E 3 {\displaystyle \mathbb {E} ^{3}} . Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R 3 {\displaystyle \mathbb {R} ^{3}} upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself. Knots can be described in various ways...

Read on Wikipedia · Image Exhibit made by Estes Objethos Atelier, photo by Rodrigo.Argenton, CC BY-SA 4.0