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Mathematics

Hyperbolic Geometry and the Poincaré Disk Model

Quick fact

In the Poincaré disk, the 'straightest' lines are actually circular arcs that meet the boundary at right angles, and the sum of a triangle's angles is always less than 180°—famously, the bigger the triangle, the smaller its angle sum.

Why this is interesting

You’ve probably learned that parallel lines never meet. But what if they could? In a curved world, the rules change—and the Poincaré disk lets you see how.