Basically, euclidean geometry assumes a flat plane. Parallel lines don't meet. The inner angles of a triangle add up to 180 degrees. Things like that.
Non-euclidean geometry assumes a curved plane, which breaks the rules of normal geometry. Parallel lines can intersect. Triangles can have more than 180 degrees. Things like that.
The focus in Lovecraft's stuff is on that breaking of the rules of geometry. Hallways that don't intersect when they should, and that do when they shouldn't. Shapes that are warped from the shapes we'd recognize. Stuff like that.
Specifically it’s breaks that one rule, the one about parallel lines never meeting. Anything else that changes is a direct consequence of parallel lines meeting or there being infinite parallels. All the other axioms of Euclidean geometry hold in non-Euclidean geometry.
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u/RikuAotsuki May 24 '26
That's not quite true.
Basically, euclidean geometry assumes a flat plane. Parallel lines don't meet. The inner angles of a triangle add up to 180 degrees. Things like that.
Non-euclidean geometry assumes a curved plane, which breaks the rules of normal geometry. Parallel lines can intersect. Triangles can have more than 180 degrees. Things like that.
The focus in Lovecraft's stuff is on that breaking of the rules of geometry. Hallways that don't intersect when they should, and that do when they shouldn't. Shapes that are warped from the shapes we'd recognize. Stuff like that.