Non-Desarguesian plane
Okay, so let's imagine we live in a world with a special kind of paper that we use to draw things. This paper is called a plane. It's like a flat surface that we can draw lines and shapes on.
Now, some people have discovered that there are different kinds of planes that we can draw on. One kind is called a Desarguesian plane. This kind of plane is very organized. It has some rules that we can follow when we draw things on it.
But some people have also discovered a different kind of plane called a non-Desarguesian plane. This kind of plane doesn't follow the same rules as the Desarguesian plane. It's more like an alternative way of drawing things.
For example, let's say we want to draw a square on a Desarguesian plane. We would start by drawing two lines that are perpendicular to each other. Then we would draw two more lines that are perpendicular to those lines. The square would be formed by the points where these lines intersect.
But on a non-Desarguesian plane, we might have to do things differently. We might have to draw lines that don't meet or lines that seem to intersect in strange ways. This sounds confusing, but it can actually be really interesting! It means we can draw things that we couldn't draw on a Desarguesian plane.
In summary, a non-Desarguesian plane is a different kind of paper where we can draw things in a different way than on a Desarguesian plane. It's like having two different paintbrushes that we can use to create different kinds of art!
Now, some people have discovered that there are different kinds of planes that we can draw on. One kind is called a Desarguesian plane. This kind of plane is very organized. It has some rules that we can follow when we draw things on it.
But some people have also discovered a different kind of plane called a non-Desarguesian plane. This kind of plane doesn't follow the same rules as the Desarguesian plane. It's more like an alternative way of drawing things.
For example, let's say we want to draw a square on a Desarguesian plane. We would start by drawing two lines that are perpendicular to each other. Then we would draw two more lines that are perpendicular to those lines. The square would be formed by the points where these lines intersect.
But on a non-Desarguesian plane, we might have to do things differently. We might have to draw lines that don't meet or lines that seem to intersect in strange ways. This sounds confusing, but it can actually be really interesting! It means we can draw things that we couldn't draw on a Desarguesian plane.
In summary, a non-Desarguesian plane is a different kind of paper where we can draw things in a different way than on a Desarguesian plane. It's like having two different paintbrushes that we can use to create different kinds of art!