The eccentricity of an ellipse is equal to the time dialation coefficient (or its inverse?) where a is any value representing the velocity of light and b is a value less than a (obviously) representing some value of velocity. I know how the relativistic transformation is derived, but dont know how the eccentricity of an ellipse is derived, perhaps that is why it surprised me. I just find it pretty neat how a ratio between distances in a simple shape have implications in special relativity.