Have you ever wanted to fight Euclid? Is that something you've ever felt the need to do? What if I told you he lived in the year 300 B.C. and all of the information we use about shapes are his fault? Think about it. This guy was so good at knowing what a line was that we still use almost all of his theorems and proofs. The worst thing is actually stuff that Euclid didn't do.
Geometry is split into two categories. Stuff that Euclid did, and stuff that Euclid didn't do. Euclid did all of the basic shape stuff, so people pretty much made up other categories of math to figure out. Why the helc would you make stuff up just to figure it out?!
Anyway what defines what is and is not Euclidean is how the math interpretation defines a line. The geometry we do defines a line as a line, but other types of geometry define lines as all kinds of weird things. It's basically a game of find a geometry type and guess what a line is.
Sometimes a straight line is actually a parabola within a circular plane apparently.
Sometimes a straight line is just a circle for some reason.
Sometimes a straight line is just a single point in a 3 dimensional plane or something I dunno.
At some point, someone is just going to point at a shape like a triangle and say, "That's a line," and other math people are going to say, "I see that. How does it work?" And they'll spend like 200 years trying to figure it out even though it effectively has no application but we know it exists so it must be important. It's like looking at your calculator and saying, "In what dimension does this look like my grandmother," and astral projecting to find out.
Thus Euclid has doomed us to forever figure out how he's wrong. He was so good and so very correct at math that people just can't deal with it so they try to disprove it. That's like the exact opposite of the attitude towards Freud (Who was so bad at psychology, and so, sooo wrong, that most of our psychological breakthroughs come from people trying to disprove his theories. Seriously some of them are really weird that guy had a serious problem. Like the Oedipus complex thing. Why? Who told you that that was something you should ever say? Was this from personal experience? Was he just so disconnected from his own humanity that he thought it was normal??? WHAT THE FUUu.) Please don't punch Euclid. Also try out this non-Euclidean geometry simulation thing and punch it's creator.
