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Is the Cayley graph of a free group dense on the Poincare disc? up vote 1 down vote favorite In other words, every point inside the disc corresponds to a word (possibly of infinite length) of the free group; Is that correct? With this embedding:

The Poincaré disk model or Poincaré ball model,... - MATHEMATICS & NATURE

The Poincaré disk model or Poincaré ball model, also called the conformal disk model, is a model of n-dimensional hyperbolic geometry in which the points of the geometry are in an n-dimensional disk,.