Poincaré disk model

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Poincaré disk model

Summary

The Poincaré disk model is a way to represent hyperbolic geometry inside a normal-looking unit circle. In this model, the entire infinite hyperbolic plane is squeezed into the interior of a disk, where points near the edge are “infinitely far away” in hyperbolic terms. Straight lines (called geodesics) appear as circular arcs that meet the boundary circle at right angles, or as diameters of the disk. 

A key feature is that it is conformal, meaning it preserves angles, so shapes look locally correct even though distances are distorted. This makes it especially useful in mathematics for visualizing hyperbolic geometry in a way that feels intuitive, even though the underlying space behaves very differently from Euclidean geometry.

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