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Mathematics

Hyperbolic Geometry Beyond the Poincaré Disk Model

Quick fact

The hyperboloid model represents hyperbolic geometry as a curved surface in Minkowski space, and it is the model used in special relativity to describe velocity space—where rapidities add linearly along a line of constant direction.

Why this is interesting

You've probably seen the famous Poincaré disk—circles shrinking to the edge—but did you know that this is only one of several ways to draw the hyperbolic plane? Some models stretch it out, others shrink it, and one even treats it as a curved surface in 3D.