It is a triangle. The abstraction of lines in non-Euclidean geometry are geodesics and just like three lines form a triangle, so do the geodesics. If you walked along the earth's surface from the equator to the North Pole and back, taking 90 degrees angles every time, you will have felt that you made a triangle by walking straight in three directions.
The reason the angle sum can be more than 180 degrees is that the sphere has a positive curvature. If you want one with negative curvature and less than 180 degrees angle sum, try to make one on the side of the hole on a torus (look up its curvature if my explanation was lacking).
The wonders of non-Euclidian geometry. Yes, this is a triangle, but as it exists in a non-Euclidian space, some rules you learned about in school which mostly teach Euclidian geometry, don't apply.
I was reading Matt Parker's new trigonometry book and they made some remark about triangles in spherical geometry and I went "wait, what if you did this"
There's a theory about Alice in Wonderland that Lewis Carroll was satirizing the absurdity of the increasingly abstract mathematics that was popping up at the time. Now, I don't think that theory holds weight--Alice in Wonderland doesn't need to be anything other than a whimsical children's book--but he did apparently write some things along those lines. This post is a pretty good example of something that would throw him into a rage.
Would the southern shape here also qualify as a triangle?
What if you went the short way instead of the long way, creating the spherical triangle people usually use - then is the "outside" portion of the triangle itself another triangle?
If a shape has 3 corners and 4 edges, it is incomplete or open and therefore not a shape yet but a collection of edges (or possibly, two triangles that share an edge).
A shape with 4 corners and 3 edges is not possible. An edge cannot have a corner in the middle of it, that would make it two edges.
Why the down votes? Bro asking a question and being legit curious, don't be hating on someone that's looking to challenge what they know just because it's trivial to you.
Just noticed in euclidean geometry, for any two line segments touching at a point there is exactly one triangle you can draw, i.e. a triangle is uniquely described by any two of its legs. In spherical geometry, there are two choices for the third leg!
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.
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.
You didn’t complete the great circles. When you draw 3 pairwise intersecting great circles you produce 2 spherical triangles on opposite sides of the sphere.