Curve orientation

Imagine that you are looking at a really cool picture of a curved line. This line can go up, down, left, or right, but it always comes back to where it started. When we talk about curve orientation, we are talking about which direction the line goes.

Here's a simple way to check curve orientation. Take your right hand and make it into a fist, with your thumb sticking up. Imagine that your fist is a little person walking along the curve. If the curve goes in the same direction as your fingers (towards your pinky), then the little person can walk along the curve without crossing over it. This is called a "positive" curve orientation. If the curve goes in the opposite direction (towards your thumb), then the little person cannot walk along the curve without crossing over it. This is called a "negative" curve orientation.

Sometimes you might see a curve that doesn't have an orientation. This usually means that the curve is actually made up of two or more curves going in opposite directions. But most curves do have an orientation, and it's important to keep track of it when you're doing math or science. For example, if you're studying electricity, positive and negative orientation can affect the flow of current in a circuit.

In summary, curve orientation is just a fancy way of saying which direction a curve goes. You can check whether a curve has a positive or negative orientation by imagining a little person walking along it with their thumb up.