Caption: Differential geometry uses the techniques of calculus in the analysis of geometry.

In the displayed image, differential geometry is exemplified by a hyperbolic triangle on hyperbolic paraboloid (a saddle shaped surface) and two diverging ultraparallel lines.

The hyperbolic triangle has vertex angles that sum to less than 180°.

The ultraparallel lines have a unique line that is perpendicular to the both of them at their point of closest approach.

Credit/Permission: User:LucasVB, 2007 / Public domain.
Image link: Wikipedia.
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File: Relativity file: differential_geometry.html.