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.

  • Tony N@lemmy.ml
    137·
    3 months ago

    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°.

    • Blóðbók@slrpnk.net
      40·
      3 months ago

      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.

      • SkyNTP@lemmy.ml
        21·
        3 months ago

        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.

        • bdonvr@thelemmy.club
          4·
          3 months ago

          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.

        • Urist@lemmy.mlEnglish
          3·
          3 months ago

          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.