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.
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Yes, but to be more specific, it is a spherical triangle.
Spherical isosceles triangle, in this particular example.
This is an example of non-Euclidean geometry. In this non-Euclidean space, it is a triangle.
I am pleased to see that there is a section on Lovecraft in that article. He really loved his non-Euclidian geometry
as well as being really aggressively racist
This inevitably comes up every time he is mentioned. Yes, he was very racist, even for the time. That mainly came forth from the fact that he was a very socially disturbed and scared person. Which isn’t an excuse, nu i think we should be able to appreciate the amazing writing and the influence he has had on the literary (horror) landscape without just focusing on the fact that he was racist.
Don’t worry. Give it half a millenium and we all will have been racist against dogs.
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.
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).
EDIT: Picture for reference:
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?
I didn’t even think of that. Another good question!
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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!
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.
Yes and I hate it >:(
Doritos are triangles so sure
I’m not asking about a Dorito shape.
I’m sorry for your loss
Spherical geometry - good times…
Yep, it’s a triangle. You can also make one with three right angles on a sphere!
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.
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.
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.
Well technically a line isnt a curve or vice versa. A possible projection of this 3d shape onto a 2D plane is a triangle, though, yes.
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Looks like a w to me.
Cowboy hat, maybe?
Edit: No, more like a Mountie hat.
