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.

  • RightHandOfIkaros@lemmy.worldEnglish
    21·
    3 months ago

    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.

    • towerful@programming.dev
      2·
      3 months ago

      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.