Is this a triangle?
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?
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.
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.
I felt like adding something about the specific case of 180° between edges and a vertice.
Makes sense.
And I guess too many vertices means an open set of edges (ie not close, this not a shape).
I was kinda hoping for a strange edge case, like a mobius strip or Klein bottle.
I guess a mobius strip is a 2d representation of a 1d paradigm. And a klein bottle is a 3d representation of a 2d paradigm.
It would be too much to ask of a 1d representation of a ??d paradigm.
I feel my comment adds to the discussion and wants more details.
But it was too simply phrased.
I guess the details of such a question should be obvious. And if you need the details, the question doesn’t actually add the the discussion… It just seems idiotic!
I felt like there might be a really cool scenario where a vertice isn’t considered a vertice.
Like, there actually might be some case on a 2d plane “where actually” applies.
I’m fine being wrong
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?
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.
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?
There’s an entire field of science projecting shapes from the surface of a sphere onto a planar surface going back centuries.
Suffice it to say, I don’t know you’d have to talk to a map-nerd.
Two things I need to ask:
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