In physics, there's a very big difference between the way things look, and they way they calculate.
Math doesn't care how i draw things, it only cares about the numbers, and even numbers are surprisingly flexible because you can change the formulas.
A very simple example: imagine i make the entire universe twice as big, you and your ruler included. Would you notice?
The math/physics can be tweaked so it also doesn't notice.
Have a look at
https://troolon.com It shows physics working on a variety of differently shaped earths.
- coordinate transformations can turn any shape into any other shape
- coordinate transformations don't break physics
-> physics can be made to work on any shape universe (have a look at
http://troolon.com for pictures)
-> There is no test to differentiate between the shapes. In reality we can only observe/measure the physical properties, not the shape.
So have a look around you and try these two views: i'm standing on a globe and lightrays are straight,
or you could say: i'm standing on a flat plane, and light curves to exactly counteract the missing curve.
Your eyes wouldn't be able to tell the difference and there's no physical test to distinguish between the two views, it's just a matter of perception.
It's like the old question: Am i moving, or is the entire universe moving around me? It's just a matter of how you look at the world.
Also this result shouldn't be very surprising. The universe could already be a sphere, a simulation, have no shape (QM), be a restored backup from 5 minutes ago ... We will simply never know the shape of the planet. It can be flat, it can be a globe or even a velociraptor.