Curved line in geometry? - Answers

In plane, or Euclidean geometry, a line usually means a straight line and a cure often refers to something else. A semicircle would be a curved line for example. But, imagine, and it should not be hard since it is reality, that we DO NOT live on a flat surface. We live on something more like a sphere. The lines are now defined as great circles. Great circles are line that run along the surface of the sphere and cut it into two parts. Imagine a plane that goes through the center of the sphere and cuts it in half. The intersection of the plane and the sphere is a great circle. These lines are not the straight lines we saw in plane of Euclidean geometry. One big difference is that any two or more will intersect. In other geometries, one called hyperbolic geometry, the lines are either traditional vertical lines or semicircles that intersect the x axis. So what I am trying to say is that curved lines depends on the geometry you are talking about and there are many of them. In Euclidean geometry we define a line as a straight curve. So the idea of a curve is more general and a line is a specific case. It has no height or width.