4. Geometry of curved spaces

‘Geometry of curved spaces’ shows that the curvature of a curve is an extrinsic property that is visible to people when it is viewed sitting on the plane and can be defined as a curve on the Euclidean plane. German mathematician Carl Friedrich Gauss discovered that curvature is an intrinsic property of the surface in 1828. Gauss called it Theorema Egregium, which translates from Latin as Remarkable Theorem. The extrinsic curvature of curves, defines Gaussian curvature can be computed intrinsically. Higher-dimensional generalizations of surfaces are called manifolds.