A curve or surface may be extrinsically studied while embedded in Euclidean space, its structure being inherited from the ambient (i.e. surrounding) space. Intrinsic properties of the curve or surface, such as area or curvature, are properties determined by its metric properties and so independent of a particular embedding and are preserved by isometries. An intrinsic approach may be preferred when embeddings are difficult or even impossible; for example, the hyperbolic plane cannot be isometrically embedded in ℝ³.