Determine whether the following figure is a closed or an open curve.
In everyday life, we use the word curve to mean a line that isn’t straight. So we’d say that each of these are examples of curves. They’re not straight. But as a mathematical word, the word curve means something slightly different. A curve is any line straight or otherwise. So we could also say that this is an example of a curve. And this is an example of a curve, even though in everyday life we’d use the word straight to describe these lines. In maths, they’re all curves.
Our question gives us an example of a curve and asked us to think about whether it’s a closed or an open curve. What makes a curve open or closed? What if we think about taking our pen for a walk? An open curve is where we start somewhere and we end up somewhere else. A closed curve is where we start somewhere and we end up back where we began. And because the curve is closed, it makes a shape. In this case, it’s a circle. So our question is really asking if we start at one end of this curve and follow it, will we end up back where we started or in a new position?
Let’s trace the curve to find out which sort of curve it is and probably see which particular curve whether we’re likely it to end up back where we started or not. We seem to be curving inwards. And so we can see that we’re going to end up in a different place. Remember that when we start in one position and end in a different position, we have drawn an open curve. So we can definitely say that this curve is an open curve. This is where we started. And this is where the curve ended. And so our answer to the problem is that the figure is an open curve.