/lit/ - Literature

>>20298535
Sorry I >>20299213 I take back what I said about this quote,
>the universe is actually a sphere because geometry refutations began that actually the 5th axiom from Euclid about parallel lines never meeting is false
I've never read Karamazov but I'm not sure what he's referring to here. I don't know if elliptic or hyperbolic geometry necessarily implies that the universe "is a sphere" but they do imply that Euclid's 5th postulate is false in the geometry of our universe

However keep in mind that Euclid was well aware about his assumptions. He tried to retroactively refute non-Euclidean geometries by trying to use Reductio ad absurdum to show that, if the 5th postulate is false, you get a variety of bizarre, barely believable theorems.

Here's another quote from Roger Penrose,
>A little after Saccheri, the highly insightful mathematician Johann Heinrich Lambert (1728-1777) also derived a host of fascinating geometrical results from the assumption that Euclid's fifth postulate is false, including the beautiful result mentioned that gives the area of a hyperbolic triangle in terms of the sum of its angles
Which is something you can't do in Euclidean geometry.