 The fact that the Gaussian curvature of a surface at a point is intrinsic means that it is entirely determined by measurements in the surface and does not involve any question of a third dimension or the ambient space embedding the surface. The property of Gaussian curvature does not depend on how the surface is located in space, but only on intrinsic properties of its metrics. That is to say, important properties of curved surfaces remain invariant even if one bends the surface isometrically (without breaking, stretching, or folding it up). One such thing that remains invariant is the geodesics on the surface, i.e., the lines of shortest distance (lying entirely on the surface). In the case of a cylinder, the geodesics are the vertical lines, horizontal lines (circles), and helices around it —and these lines all come from straight lines on the plane that is ‘rolled up’ to form the cylinder. 