What is a Closed Curve?

Instructor: Mark Boster
Think you can figure out what a closed curve is just by looking at its name? You might be surprised! In this lesson, we will look at the two types of closed curves, simple and not simple, and learn exactly what shapes are considered closed curves.

It's Closed

Samuel needed to get new shoes. His father took him to the shoe store, but it was closed, and he couldn't get in.

Fido, the dog, was in his cage. He wanted to get out but couldn't because it was closed.

Shapes that have no way in or out are called closed curves.

Closed Curves

A closed curve is any design that has no end points drawn on a flat surface . In other words, if you draw a design, without lifting your pencil, and end at the point you began, it would be a closed curve. There is no way in or out of the shape.

An Example of a Closed Curve

Now why don't you try it?

Not Just a Curve

A closed curve doesn't even have to be a curve! What? Yes! A square is a closed curve. You can't get in it. You can't get out of it. It is a design with no endpoints, and it is on a flat surface. So is a circle, a triangle a hexagon, and anything else you can draw without lifting your pencil and that ends where it began! Easy, huh? Why don't you draw another one now?

Closed Curves

Simple Closed Curves

Even though a closed curve is one drawn without lifting your pencil and ending where you began, there are two different types of closed curves. There are those which are simple, and those which are not simple. Simple closed curves are closed curves which do not have lines that cross over themselves. If it is not simple, it does cross over itself.

Look at the 'Closed Curves' image. The star, arrow, diamond, and lightning bolt do not have lines that cross. They are simple closed curves. The other two images, the green one and the orange one, have lines that cross, and therefore, are not simple closed curves.

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