# What does intrinsic and extrinsic mean?

When I read books of geometry, I sometimes find the term "intrinsic" and "extrinsic" but don't understand them precisely.

What are definitions of them? Are intrinsic properties more important than extrinsic properties?

• could you give an example of these books' usage? – ziggurism Nov 17 '17 at 13:03
• Can you explain what you didn't understand or found unsatisfying when you searched for the terms in the context of differential geometry? For example, I think that the beginning of Wikipedia's page of differential geometry of surfaces has a good first explanation (at the time of this comment). – Mark S. Nov 17 '17 at 13:20
• Gaussian curvature is intrinsic one. – marimo Nov 17 '17 at 13:20
• @marimo: But for surfaces in $\Bbb R^3$, Gaussian curvature is defined extrinsically. So it's one of Gauss's deep results that it in fact does turn out to be intrinsic (i.e., dependent only on the metric and not on the embedding). – Ted Shifrin Nov 17 '17 at 16:54