I would have asked this on a math community but I couldn’t find an active one.
In a spherical geometry, great circles are “straight lines”. As such, a triangle can have two or even three right angles to it.
But what if you go the long way around the back of the sphere? Is that still a triangle?
(Edit:) I guess it’s a triangle! Fair enough; I can’t think of what else you would call it. Thanks, everyone.
The term you are looking for to describe such a shape is technically “spherical polygon”. Triangles are impossible in speherical geometry since the sum of the angles would always be greater than 180°.
There is no rule that the angles of a triangle add to 180 degrees. It only holds true in Euclidean geometry, which this is not.
I think this is debatable. If it was not, then the answer to OP’s question would be obvious, and this thread would be uninteresting. The words we use carry a lot of unwritten baggage.
I think OP clearly has an inkling of non-euclidian to even ask what they did, so I’m not sure euclidian rules are relevant to the discussion. It seems they know of it but non-euclidian geometry is not intuitive so this isn’t obvious to most.
The answer is obvious. Depending on the curvature of the object the triangles have higher or lower than 180 degrees angle sums. Flat space just happens to have 0 curvature.