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What does a cat in box, a fish in a bowl, a man in a box, and a ship in a bottle have to do with geometry?

man trapped in a box

Have you ever been in a really really tight space, like a box? Well, if you have been in a really tight box, a geometry teacher might say that you were inscribed, and that the box was circumscribed.

In this geometry lesson, you will see the words inscribed and circumscribed quite a bit. The words sound alike because they are closely related to each other. They go hand in hand. Even though the two words are related, you'll need to be able to quickly remember which meaning goes with which word.

Before we get into the meat and potatoes of a really detailed definition, let's talk about it in everyday terms. Here is a really simple way to understand what inscribed and circumscribed mean:

INscribed = INside

So, circumscribed must be the opposite of that:

CIRCUMscribed = OUTside

The word circumscribed might have reminded you of another word that has to do with a circle: circumference. You might remember that a circle's circumference is the distance around the outside of the circle. Again, think:

CIRCUMscribed = CIRCUMference = OUTside

So if an object or shape is on the inside, then it is inscribed. If an object or shape is around something or on the outside, then it is circumscribed. Click through the tabs below to see if you can use the words correctly. The first one is done for you.

Example 1

Example 2

Example 3

Example 4

Man trapped in a box.Here is a picture of a man trapped in a box.

The man is inscribed.

The box is circumscribed.

Here is a cat and a box. The a cat is happily and snugly in a box.

Cat and a box

Which one is inscribed, and which one is circumscribed?

The cat is inside the box, so the cat is inscribed.
The box is outside, or around, the cat. The box is circumscribed.

Here is a ship in a bottle.

Ship in a bottle.

Which is circumscribed? The ship or the bottle?

The bottle is circumscribed. The bottle is outside and surrounding the ship.
The ship is inscribed.

Here is a fish in a bowl. What's inscribed, and what's circumscribed?

Fish in a bowl of water

The fish is inscribed (inside), and the bowl is circumscribed (outside and/or around).

Now, we are ready to move on into the nitty-gritty of inscribed and circumscribed objects in geometry.