Winding number

Have you ever walked around in circles? Maybe you walked around a tree or a big rock, or just went round and round in a circle on the playground. When you did this, did you keep track of how many times you went around? The winding number is kind of like keeping track of how many times you went around in a circle.

Now, imagine you are looking at a shape or curve on a piece of paper. If you start following the curve and imagine that you are walking on this curve, you might notice that the curve goes around some points more than once. Some points might even be completely enclosed by the curve. These points are called singular points.

The winding number tells us how many times the curve goes around a singular point. It is like counting how many times you go around the tree or the rock when you are walking in a circle. But instead of saying "one, two, three," we use the winding number to keep track of how many times the curve goes around the singular point.

So, if we have a curve that goes around a singular point once, we say the winding number is 1. If it goes around twice, the winding number is 2, and so on. If the curve doesn't go around the singular point at all, the winding number is 0.

The winding number is important in math because it can help us understand the properties of curves and shapes. It can tell us if a curve is closed or not, or if two curves intersect each other. By knowing the winding number, we can better understand how shapes behave and how they are related to each other.