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  2. Normal plane (geometry) - Wikipedia

    en.wikipedia.org/wiki/Normal_plane_(geometry)

    The normal section of a surface at a particular point is the curve produced by the intersection of that surface with a normal plane. [1] [2] [3] The curvature of the normal section is called the normal curvature. If the surface is bow or cylinder shaped, the maximum and the minimum of these curvatures are the principal curvatures.

  3. Normal (geometry) - Wikipedia

    en.wikipedia.org/wiki/Normal_(geometry)

    For a plane given by the general form plane equation + + + =, the vector = (,,) is a normal. For a plane whose equation is given in parametric form (,) = + +, where is a point on the plane and , are non-parallel vectors pointing along the plane, a normal to the plane is a vector normal to both and , which can be found as the cross product =.

  4. Euclidean planes in three-dimensional space - Wikipedia

    en.wikipedia.org/wiki/Euclidean_planes_in_three...

    Plane equation in normal form. In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space. A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin.

  5. Plane (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Plane_(mathematics)

    Plane equation in normal form. In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space. A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin.

  6. Hesse normal form - Wikipedia

    en.wikipedia.org/wiki/Hesse_normal_form

    In analytic geometry, the Hesse normal form (named after Otto Hesse) is an equation used to describe a line in the Euclidean plane, a plane in Euclidean space, or a hyperplane in higher dimensions. [ 1 ] [ 2 ] It is primarily used for calculating distances (see point-plane distance and point-line distance ).

  7. Frenet–Serret formulas - Wikipedia

    en.wikipedia.org/wiki/Frenet–Serret_formulas

    The osculating plane has the special property that the distance from the curve to the osculating plane is O(s 3), while the distance from the curve to any other plane is no better than O(s 2). This can be seen from the above Taylor expansion. Thus in a sense the osculating plane is the closest plane to the curve at a given point.

  8. Plane equation - Wikipedia

    en.wikipedia.org/?title=Plane_equation&redirect=no

    Redirect to: Euclidean planes in three-dimensional space#Point–normal form and general form of the equation of a plane

  9. Distance from a point to a plane - Wikipedia

    en.wikipedia.org/wiki/Distance_from_a_point_to_a...

    The vector equation for a hyperplane in -dimensional Euclidean space through a point with normal vector is () = or = where =. [3] The corresponding Cartesian form is a 1 x 1 + a 2 x 2 + ⋯ + a n x n = d {\displaystyle a_{1}x_{1}+a_{2}x_{2}+\cdots +a_{n}x_{n}=d} where d = p ⋅ a = a 1 p 1 + a 2 p 2 + ⋯ a n p n {\displaystyle d=\mathbf {p ...