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Definition of DIFFERENTIAL GEOMETRY
: a branch of mathematics using calculus to study the geometric properties of curves and surfaces
First Known Use of DIFFERENTIAL GEOMETRY
Field of mathematics in which methods of calculus are applied to the local geometry of curves and surfaces (i.e., to a small portion of a surface or curve around a point). A simple example is finding the tangent line on a two-dimensional curve at a given point. Similar operations may be extended to calculate the curvature and length of a curve and to analogous properties of surfaces in any number of dimensions.