What can be a tool, an abstract geometric surface, and a means of transportation?
Riemannian connection on a surface space rolling without slipping or twisting on a horizontal plane. The point of contact will describe a curve in the plane and on the surface. As for the sphere, the usual curvature of the planar curve equals the geodesic curvature of the curve traced on the surface. This geometric way of viewing parallel transport can also be directly expressed in the language of geometry. The envelope of the tangent planes to "M" along a curve "c" is a surface with vanishing Gaussian curvature, which by Minding's theorem, must be locally isometric to the Euclidean plane. This identification allows parallel transport
Inequality of arithmetic and geometric means Inequality of arithmetic and geometric means In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same. The simplest non-trivial case — i.e., with more than one variable — for two non-negative numbers and , is the statement that with equality if and only if . This case can be seen