In Euclidean space, there can be several definitions that makes a straght line:
- Line of shortest distance between two points
- Line that is linear, i.e with the points satisfying a linear equation
- Line of zero curvature everywhere
- Line with constant curvature that is equal from both sides
The Wikipedia article states:
In geometry, it is frequently the case that the concept of line is taken as a primitive.
When one enters non-Euclidean geometry, are the above definitions consistent with each other? Definition 1, for example, becomes a geodesic.