Elliptic surface

Imagine you have a big round ball, like a basketball. Now, imagine you draw a bunch of different shapes, like squares, triangles, and circles, on this ball. These shapes are made up of straight lines and curved lines, and they are all different sizes and orientations.

Now, imagine that each of these shapes on the ball represents a point on a graph. This graph is called an elliptic surface. The cool thing about an elliptic surface is that it has a special point called the "origin." This origin is like the very center of the ball.

When you look at the shapes you drew on the ball, you will notice that some shapes are connected to each other. This means that when you travel along these shapes, you will end up at a different shape. These connected shapes are called "fibers" in an elliptic surface. They can be long or short, thick or thin, and they can have different shapes too.

Now, let's imagine that you take a pencil and start drawing a line on the ball, connecting all the points that are connected by the fibers. This line is called a "fiber over a point." This line is really special because it can curve and twist in all different directions.

So, when you look at an elliptic surface, you see a big round ball with lots of different shapes drawn on it. These shapes represent points on a graph, and they are all connected by fibers. You can also draw lines called fibers over points that twist and turn. Just like a fun puzzle, an elliptic surface helps us understand how all these shapes and lines are related to each other.