Edge-of-the-wedge theorem
Okay kiddo, imagine you have a big piece of cheese. Now, you want to cut it into smaller pieces. You decide to use a knife to slice through the cheese.
But wait! The knife isn’t flat, it’s shaped like a wedge. This means that when you slice the cheese, the wedge part of the knife starts cutting before the flat part.
Now, let’s say you want to know how much of the cheese you’ve sliced through with the wedge part of the knife. This is where the edge-of-the-wedge theorem comes in!
It tells you that the area you’ve sliced through with the wedge part of the knife, compared to the area you would have sliced through with a flat knife, is equal to the ratio of the length of the arc on the cheese that the wedge part of the knife has cut through, compared to the circumference of the cheese.
So basically, this theorem helps you figure out how much of your cheese you’ve sliced through using a wedge-shaped knife. Pretty cool, huh?
But wait! The knife isn’t flat, it’s shaped like a wedge. This means that when you slice the cheese, the wedge part of the knife starts cutting before the flat part.
Now, let’s say you want to know how much of the cheese you’ve sliced through with the wedge part of the knife. This is where the edge-of-the-wedge theorem comes in!
It tells you that the area you’ve sliced through with the wedge part of the knife, compared to the area you would have sliced through with a flat knife, is equal to the ratio of the length of the arc on the cheese that the wedge part of the knife has cut through, compared to the circumference of the cheese.
So basically, this theorem helps you figure out how much of your cheese you’ve sliced through using a wedge-shaped knife. Pretty cool, huh?