Hyperbolic Poincaré Disk

In Hyperbolic Geometry, the sum of angles in a triangle is always less than 180 degrees. We use the Poincaré Disk Model, where "lines" (geodesics) are circular arcs perpendicular to the boundary.

Gauss-Bonnet Theorem: The "defect" (180 - sum) is proportional to the area of the triangle times the curvature. Instructions: Drag the red vertices ($A, B, C$) to reshape the triangle. Observe how the angle sum drops as points move toward the boundary (infinity).