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  2. Tangent developable - Wikipedia

    en.wikipedia.org/wiki/Tangent_developable

    Tangent developable of a curve with zero torsion. The tangent developable is a developable surface; that is, it is a surface with zero Gaussian curvature.It is one of three fundamental types of developable surface; the other two are the generalized cones (the surface traced out by a one-dimensional family of lines through a fixed point), and the cylinders (surfaces traced out by a one ...

  3. Equiareal map - Wikipedia

    en.wikipedia.org/wiki/Equiareal_map

    In the context of geographic maps, a map projection is called equal-area, equivalent, authalic, equiareal, or area-preserving, if areas are preserved up to a constant factor; embedding the target map, usually considered a subset of R 2, in the obvious way in R 3, the requirement above then is weakened to:

  4. Torsion of a curve - Wikipedia

    en.wikipedia.org/wiki/Torsion_of_a_curve

    Animation of the torsion and the corresponding rotation of the binormal vector. Let r be a space curve parametrized by arc length s and with the unit tangent vector T.If the curvature κ of r at a certain point is not zero then the principal normal vector and the binormal vector at that point are the unit vectors

  5. Differential geometry of surfaces - Wikipedia

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

    The differential geometry of surfaces is concerned with a mathematical understanding of such phenomena. The study of this field, which was initiated in its modern form in the 1700s, has led to the development of higher-dimensional and abstract geometry, such as Riemannian geometry and general relativity. [original research?]

  6. File:Geometry for Elementary School.pdf - Wikipedia

    en.wikipedia.org/wiki/File:Geometry_for...

    2007-04-25 18:16 Whiteknight 1275×1650× (1355429 bytes) A PDF version for [[Geometry for elementary school]], based on the print version of that book. Created by myself using PDF24. Created by myself using PDF24.

  7. Riemannian connection on a surface - Wikipedia

    en.wikipedia.org/wiki/Riemannian_connection_on_a...

    In mathematics, the Riemannian connection on a surface or Riemannian 2-manifold refers to several intrinsic geometric structures discovered by Tullio Levi-Civita, Élie Cartan and Hermann Weyl in the early part of the twentieth century: parallel transport, covariant derivative and connection form.

  8. Differentiable curve - Wikipedia

    en.wikipedia.org/wiki/Differentiable_curve

    The differential-geometric properties of a parametric curve (such as its length, its Frenet frame, and its generalized curvature) are invariant under reparametrization and therefore properties of the equivalence class itself. The equivalence classes are called C r-curves and are central objects studied in the differential geometry of curves.

  9. Mean curvature flow - Wikipedia

    en.wikipedia.org/wiki/Mean_curvature_flow

    In the field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space).

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