# What's the difference between hyperbolic length and hyperbolic distance?

From what I understand, the hyperbolic distance between two points in hyperbolic space is the length of the line(semicircle) that connects those two points.

The hyperbolic length then would be the sum of all the little tangents on any curve connecting those two points.

I am having trouble differentiating the two ideas and don't even know if they're right to be honest.

• Think about the corresponding Euclidean concepts (Euclidean lines are straight lines instead of circles intersecting the boundary, of course). Distance is a thing associated to two points, and is the length of the shortest curve connecting them. The length of a curve is a property of the curve, and is given by an integral of arc-length. – Chappers Apr 5 '17 at 19:41