Incidence geometry

Incidence geometry is like playing a game of connect-the-dots! Imagine you have a bunch of dots (called points) on a piece of paper, and you connect some of them with lines (called lines or edges), but you don't draw any shapes like circles or squares.

Now, let's imagine you want to explore some cool properties of these dots and lines, like how many lines can pass through a single point, or how many points can be on the same line. This is what incidence geometry is about!

Every time a line touches a point, we call it an incidence (interaction) between the two. And if two lines intersect, they will also have an incidence. By carefully studying incidences between points and lines, we can find out a lot of interesting things about this abstract world of dots and lines.

For example, say we've discovered that every line must have at least two points on it. This means we could draw a line with only one point, but then that line wouldn't really be a line at all! We can also find out which dots and lines are connected, and see if we can create new lines by connecting dots in different ways.

In short, incidence geometry is a way to explore the relationships and properties of points and lines in a fun and exciting way – just like playing connect the dots!