Knot (Mathematics)

In mathematics, a knot is an embedding of a circle into three-dimensional Euclidean space, considered as a closed loop with no loose ends. Two knots are usually regarded as equivalent if one can be continuously deformed into the other without cutting the loop, a relation called ambient isotopy. Unlike knots in rope or string, a mathematical knot disregards physical properties such as thickness and friction, isolating the pure question of how a loop can be tangled in three-dimensional space.