At time 1:11:20, Lenny introduces the metric for ordinary flat space in the hyperbolic version of polar coordinates? Is that what he is doing here? d(tau)^2 = ρ^2 dω^2 - dρ^2. He then goes on to say that this metric is the hyperbolic version of the same formula for Cartesian space, i. e., ρ^2 dθ^2 + dρ^2 My question is what does the Cartesian version equal? It cannot equal d(tau)^2. Does it equal dS^2? That is, dS^2 = ρ^2 dθ^2 + dρ^2 And what is this telling us? Is it the formula for the distance between 2 points on a Cartesian plane in polar coordinates? I looked for a derivation of this formula online and on you-tube and couldn't find it. Can someone direct me to a "B-level" online link I can look at?