High Quality Content by WIKIPEDIA articles! Weingarten equations give expansion of the derivative of the unit normal vector to a surface in terms of the first derivatives of the position vector of this surface. These formulas were established in 1861 by German mathematician Julius Weingarten. Let S be a surface in three-dimensional Euclidean space that is parametrized by position vector r(u, v) of the surface. Let P = P(u, v) be a fixed point on this surface. Julius Weingarten (25 March 1836 in Berlin – 16 June 1910 in Freiburg im Breisgau) was a German mathematician. He made some important contributions to the differential geometry of surfaces, such as the Weingarten equations. Weingarten equations give expansion of the derivative of the unit normal vector to a surface in terms of the first derivatives of the position vector of this surface. These formulas were established in 1861 by German mathematician Julius Weingarten.

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