Reading the lecture notes of Minkowski's famous 1908 geometric unification of space and time, he introduces the "light cone" outer boundaries as the asymptotes of a two branch hyperbola that have been rotated about the time axis to form two inverted cones. Somehow his diagram evolves from a two-sheet hyperboloid to two cones,inverted to one another with their apexes at the origin of a 3D coordinate system. Time is the vertical axis extending through the center of the two cones, and is actually the product of time and the speed of light so that it is calibrated in "spatial" units i.e. light-seconds. The X and Y axes are the abbreviated representation of space, and are orthogonal to the time axis. I think he gets from the hyperboloid to the cone by approaching some limit. Can someone explain this to me and correct any misconceptions I might have conveyed here?