The discussion is about triangles in hyperbolic space. In hyperbolic space, if you keep extending a triangle's lines out by moving the intersection farther away, you'll tend toward a triangle with a constant area (pi in the article because the curve was chosen for that, you can have any arbitrary finite value you want by varying the curvature) even though the perimeter keeps going up.

If that sounds like so much technobabble, that's because this article assumed what I think is a very specific level of knowledge about hyperbolic space, as it doesn't explain what it is, yet this is one of the very first things you'll ever learn about it. So it has a rather small target audience of people who know what hyperbolic space is but didn't know that fact about triangles. If you'd like to catch up with what hyperbolic space is, YouTube has a lot of good videos about it: https://www.youtube.com/results?search_query=hyperbolic+spac... And as is often the case with geometry, videos can be a legitimate benefit that is well taken advantage of and not just a "my attention span has been destroyed by TikTok" accomodation.

Including CodeParade's explanations, which are notable in that he made a video game (Hyperbolica) in which you can even walk around in it if you want, with an option for doing it in VR (though that is perhaps the weirdest VR experience I had... I didn't get motion sick per se, but my brain still objected in a very unique manner and I couldn't do it for very long). It's been out and on Steam for a while now, so you can run through the series where he is talking about the game he is in the process of creating at the time and go straight to trying it out, if you want.