Plane–sphere intersection

Okay, let's pretend that you have a big ball in front of you, kind of like a giant beach ball. Now imagine that you have a flat piece of paper and you hold it up so that it's touching the ball at a certain spot.

When the paper touches the ball, it creates a line on the paper where it meets the ball. This is kind of like drawing a circle by tracing around the ball. This line is the intersection of the paper and the ball.

Now, instead of a ball, let's pretend that we have a different kind of round shape called a sphere. And instead of a piece of paper, we have a flat surface called a plane.

When we hold the plane up to the sphere and they touch each other, they create a circle on the plane where they meet. This is the plane-sphere intersection. It's the spot where the plane and the sphere touch each other and create a circle.

People use plane-sphere intersections in math and science to help figure out things like how to map the Earth's surface or how to design a certain kind of building. It might sound complicated, but it's really just about figuring out where a flat surface touches a round shape!