Complex projective plane

Okay, so imagine you have a piece of paper (let's call it a plane) that can stretch and bend in any way you want it to. Now imagine you have some dots (let's call them points) on this paper.

But wait! Some dots are special – they have more coordinates than just two. They have three coordinates, like (1, 2, 3). Let's call these points special points.

Now, if we were in a regular two-dimensional world, these special points would be very different from the other points. But since we're in the complex projective plane, we can make them all the same!

How? By stretching and bending the paper, of course! We can take each special point and make it so that all three of its coordinates are the same. This way, it becomes just like any other point on the paper.

This stretching and bending is called a projective transformation. It's like folding and unfolding a piece of paper until it fits into a different shape.

So now we have a plane with points of all different types, but they all look the same. That's the complex projective plane – a special kind of geometric space where points with different numbers of coordinates can be considered equal.