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.

    • bionicjoey@lemmy.ca
      10·
      2 个月前

      If you were to walk this route along the surface of the earth, you would walk in perfectly straight lines apart from the three turns.

      • I_Has_A_Hat@lemmy.world
        14·
        2 个月前

        No such thing. Even if you were walking on a surface with no change in elevation, the acceleration due to gravity would cause your path to be curved as it followed the curvature of the planet.

        • Farid@startrek.website
          9·
          2 个月前

          Curved relative to what?

          Edit: Nvm, I understood what you mean. But I think it’s a pedantic take. They obviously mean it in the context of the surface of the sphere.

    • november@lemmy.vgOPEnglish
      72·
      2 个月前

      They’re not curved; the space they’re embedded in is curved.

      • Azzu@lemm.ee
        1·
        2 个月前

        Well that depends on your definition of curved… If I look at this image from a 3 dimensional coordinate system that includes the sphere, the edges are definitely curved. Of course, if you look at this from the coordinate system “surface of the sphere” then I would agree with you. There are 2 ways to look at this and decide if it is a triangle, and the bro you responded to didn’t understand this and needs it explained.

        • bdonvr@thelemmy.club
          5·
          2 个月前

          I don’t think this is relevant. Using your first definition there is no possible way to walk in a straight line on a sphere. While true in that context I don’t think it’s what most people are meaning by “straight line”.

          • Azzu@lemm.ee
            2·
            2 个月前

            But it’s absolutely clear that the first definition is meant by the person that is being responded to. That is why the clarification is needed. This is not about “most people”, but this specific one person in this specific comment thread. “It doesn’t matter that the edges are curved?” is only said by someone that thinks in the first definition, not in the second.