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  2. Gaussian curvature - Wikipedia

    en.wikipedia.org/wiki/Gaussian_curvature

    In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ 1 and κ 2, at the given point: =.

  3. Gauss map - Wikipedia

    en.wikipedia.org/wiki/Gauss_Map

    In differential geometry, the Gauss map of a surface is a function that maps each point in the surface to a unit vector that is orthogonal to the surface at that point. Namely, given a surface X in Euclidean space R 3 , the Gauss map is a map N : X → S 2 (where S 2 is the unit sphere ) such that for each p in X , the function value N ( p ) is ...

  4. Newton's method in optimization - Wikipedia

    en.wikipedia.org/wiki/Newton's_method_in...

    Newton's method uses curvature information (i.e. the second derivative) to take a more direct route. In calculus , Newton's method (also called Newton–Raphson ) is an iterative method for finding the roots of a differentiable function f {\displaystyle f} , which are solutions to the equation f ( x ) = 0 {\displaystyle f(x)=0} .

  5. Curvature - Wikipedia

    en.wikipedia.org/wiki/Curvature

    The normal curvature, k n, is the curvature of the curve projected onto the plane containing the curve's tangent T and the surface normal u; the geodesic curvature, k g, is the curvature of the curve projected onto the surface's tangent plane; and the geodesic torsion (or relative torsion), τ r, measures the rate of change of the surface ...

  6. Differential geometry of surfaces - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry_of...

    The geodesic curvature k g at a point of a curve c(t), parametrised by arc length, on an oriented surface is defined to be [58] = ¨ (). where n(t) is the "principal" unit normal to the curve in the surface, constructed by rotating the unit tangent vector ċ(t) through an angle of +90°.

  7. Curve fitting - Wikipedia

    en.wikipedia.org/wiki/Curve_fitting

    Fitting of a noisy curve by an asymmetrical peak model, with an iterative process (Gauss–Newton algorithm with variable damping factor α).Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints.

  8. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    Note that this transformation formula is for the mean curvature vector, and the formula for the mean curvature in the hypersurface case is ~ = ( , ) where is ...

  9. Curvature form - Wikipedia

    en.wikipedia.org/wiki/Curvature_form

    Curvature form in a vector bundle. If E → B is a vector bundle, then one can also think of ω as a matrix of 1-forms and the above formula becomes the structure ...