This is a problem I'm having reading Visual Complex Analysis, page 295. If you look up "pseudosphere circles of curvature" on Google, it should be the first thing listed. On a point of a psuedosphere, there are 2 "circles of curvature", one with its center on the normal pointing out and the other with its center on the normal pointing in. 1. Is that right? 2. Does the circle with its center on the normal pointing inwards have to have its center on the axis of the psuedosphere? 3. If the answer to 2. is yes, why is this? I do not know differential geometry and hope for an answer that is as intuitive as possible. Thanks.