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Imagine that you are a two-dimensional creature. You know that the universe you live in is...

Imagine that you are a two-dimensional creature. You know that the universe you live in is either the Euclidean plane, a sphere, or a cylinder. How could you decide which is true? (Assuming that you are intelligent and have unlimited funding and patience and great technology. But of course, you can't leave your universe.) Describe any difficulties that might arise.

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Answer #1

So yeah! we have unlimited funding and great technology but I am 2 dimensional being means I can move on just forward and backward and left and right and know nothing about height. No matter, I will developed a car or some vehicle having speed of light and infinite fuel( solar charging or something) and now I will launch this car towards my east and wait. If this car never comes it means universe is infinite euclidean plane. But if car comes back to the starting point. It means universe is sphere or a cylinder.

Now launch this car towards north again wait. If car comes then universe is a sphere and if it never comes then universe is cylinder.

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