Pretty sure it's a Riemann sphere

>>8173703
this
[th is]
pronoun, plural these [th eez] (Show IPA)
1. (used to indicate a person, thing, idea, state, event, time, remark, etc., as present, near, just mentioned or pointed out, supposed to be understood, or by way of emphasis):
"This is my coat."

>>8173735

while this is pretty much /thread, does anyone else wonder what
's gonna happen if we crawl through definition of the english word? Like how long does it take before you end up in a loop or what word will reach the most word the quickest.

>>8173703

I'm gonna go with: Riemann sphere.

an imaginary sphere but I believe it might be the shape of universe

>>8173773
Its also known as riemann sphere

>>8173773

Why would you possibly believe that the universe has positive curvature?

Especially, considering that everything we know tells us that its flat.

>>8173703
It's just the complex plane projected onto a sphere. A on the complex plane sits at P(A) on the sphere, like your pic shows. Basically, you draw a line from the top of the sphere to the point on the plane, and the intersection on the sphere is where that point sits on the sphere.

>>8173703
It's a fucking sphere.

But a sphere minus a point is homeomorphic to the complex plane. Adding that extra point to the complex plane makes it into a compact space, and we consider this point to be off at infinity.

>>8173829
It doesn't really make sense to say spacetime has positive or negative curvature since that depends on the signature you choose for spacetime - positive curvature in (-+++) is negative in (+---) and vice versa. For example, it makes sense to call de Sitter space positively curved because space is spherical, but time in de Sitter space is hyperbolic, so in the (+---) convention spacetime would have negative curvature - time has negative curvature and has a + sign, space would have positive curvature but the space part of the metric gets a minus sign, so the sphere actually has negative curvature. This is the reason people working in relativity choose the (-+++) signature - it keep the curvature intuitive for the 3 spatial dimensions, but this choice is arbitrary at the end of the day. AdS space has the opposite curvature, in which space is hyperbolic and time is spherical - a 1D sphere, more commonly called a circle ; )
Also the universe IS curved, but the cosmological constant is very small. On top of that you have the curvature from gravity, which can be large but localised, and the expansion of the universe. The fact that the cosmological constant is small but positive implies that the universe is a sort of expanding dS space (at least it will do in the future when the cosmological constant dominates everything else).

That's an infinite amount of spheres. Trust me I'm a mathematician.

>>8173703
Sphere with a radius of -1/12

>>8173961
>implying -1/12th of a sphere can be physically represented

>>8173959
disregard that i suck cocks

>>8173703

Basically you take the complex plane and crumple it up like a garbage bag into a sphere shape.

The result is that any point really, really far away from the origin in complex coordinates will actually be "the point at infinity."

This means that if I go up and to the left forever, or down and to the right forever, I end up at the same point.

>>8173838
>>8174120
These. The Riemann sphere is very useful in determining what "infinity" means in the complex plane. Let the equator of the Riemann sphere be the complex plane. In your figure, points A and B are complex points. To each point on the complex plane, we can draw a line that passes through a complex point and through the surface of the Riemann sphere, which is denoted as alpha in your figure. It is also possible to construct a line that passes through A,alpha, and the top of the Riemann sphere, which is [math]P(\infty)[/math] in your figure. If we can make such a line, then you will notice that alpha and A will have a one-to-one correspondence. The point [math]P(\infty)[/math] is what you would call infinity for the complex plane.