Additions:
Additions:
{{image class="right" alt="curvature-10" title="Trumpet Geometry" url="images/curvature/Curvature-10N.gif"}}If in a small region the value of the circumference of a circle approaches ""2πr"", the geometry locally approximates a flat geometry. It has a flat //tangent space// (red). If there is no unique tangent space the geometry has a ""singularity"", as at the apex. The practical implication is that, in general relativity, a singularity is a point where we do not know how to formulate the laws of physics.
Deletions:
{{image class="right" alt="curvature-10" title="Trumpet Geometry" url="images/curvature/Curvature-10N.gif"}}If in a small region the value of the circumference of a circle approaches ""2πr"", the geometry locally approximates a flat geometry. It has a flat //tangent space// (red). If there is no unique tangent space the geometry has a //singularity//, as at the apex. The practical implication is that, in general relativity, a singularity is a point where we do not know how to formulate the laws of physics.
