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Say that I'm an ant that lives on this curved sphere.
I walk up to the vertex of the triangle at the north pole and I measure it - I find it to be 90 degrees - right?
I walk to the other two and I measure 90 degrees. Totalling 180 degrees.
Would I perceive that I was upsidedown at the south pole as compared to the north pole? I don't think so, as the space itself is curved, but if I was on a sphere in euclidian space, then I would perceive myself as upsidedown on the south pole.
So according to my ant brain, this triangle is flat, but with 270 degrees in it.
Does this sound right?
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