math stuff

In mathematics, space isn't always what it seems! There are different types of "geometric spaces," each with its own rules and properties, leading to some surprising results.

For example, we're all familiar with "Euclidean space" (basically the geometry we learn about in school). In this space, parallel lines never meet, no matter what. This is one of the fundamental principles of Euclidean geometry, established by Euclid himself!

But if we move to "projective space", everything changes. Here, parallel lines do meet at what we call the point at infinity (or improper point). 
This might sound strange, but it makes sense if you imagine "extending" the plane in all directions, including infinity. This concept is essential in fields like artistic perspective or photography, where the goal is to represent three-dimensional reality on a two-dimensional surface.

And that's not all—there are other geometric spaces too! In "hyperbolic geometry", parallel lines can diverge, while in "spherical geometry", parallel lines don't exist at all (because every "line" is actually a great circle, like the meridians on Earth).

These ideas show that geometry isn't "one-size-fits-all" but rather a set of tools to describe reality from different perspectives. Each of these spaces has practical applications, from the theory of relativity to computer graphics.

(Sorry for any mistakes, english is not my first language. I hope you enjoy these curiosities!!)