"Hyperbolic Medicine" encompasses various aspects. Human vision is hyperbolic because the space we live in is warped. Conical perspective represents images that travel at the speed of light to the observer's eye, following hyperbolic curves of space-time. There is a different hyperbolic perception according to the animal species. Human physiology is hyperbolic because it is adapted to this hyperbolic deformation of the space in which we live. That physiology can be fragmented like a magnet into smaller ones, resembling a fractal. Electromagnetic fields act on a cellular process through local hyperbolic curves. Human circadian rhythms may be in sync with those hyperbolic curves. There is a space-time relativity, perpendicular to the axis of movement of an organ, which gives hyperbolic curves. Diseases can be studied as an expansion-contraction system that moves with different speeds. In the treatment of diseases, there is the possibility of modifying the hyperbolic dimensions of a pathological physiological process, acting in its time and space of development.