Duality (projective geometry)

Duality in projective geometry is like a game of pretend with mirrors. Let's say you have a shape, like a square. You can pretend there's a mirror on one side of the square, and then you draw the reflection of the square in the mirror. This reflection is the dual of the original square.

Now, let's say you drew a line through the square. You can also pretend there's a mirror that is perpendicular (straight up and down) to this line. You can draw the reflection of the square in this mirror too. This reflection is also the dual of the original square.

But why do we do this? Well, when you make a shape's dual, you can learn things about the original shape that might not be obvious just by looking at it. For example, you might learn about the lines and points that make up the shape.

Also, sometimes it's easier to work with the dual of a shape rather than the original shape. Just like how it's sometimes easier to look at yourself in a mirror to see if your clothes are on straight!