In other words, knots are just the tame curves in Euclidean 3-space which are homeomorphic to a circle. The word “tame” here stands for a property intended to rule out certain pathological cases, such as curves with infinitely nested knotting. There is more than one way of making this mathematically precise, but we have no need for these details. A knot has a specific geometric shape, size and axis-relative position. Now imagine it to be made of flexible yet unbreakable yarn that is stretchable and shrinkable, so that it can be smoothly transformed into other knots without cutting or gluing. Since our interest in a knot is the nature of its knottedness regardless of shape, size or axis-relative position, the real focus of interest is not just the knot but all its possible transforms. A way to think of this is to imagine a knot transforming continuously, so that every possible transform is realized at some time. Then the thing of central interest would be the object that persists over time in varying forms, with knots strictly so called being the things captured in each particular freeze frame. Mathematically, we represent the relevant entity as an equivalence class of knots.