Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Umbilical_point> ?p ?o. }
Showing items 1 to 30 of
30
with 100 items per page.
- Umbilical_point abstract "In the differential geometry of surfaces in three dimensions, umbilics or umbilical points are points on a surface that are locally spherical. At such points the normal curvature in all directions are equal, hence, both principal curvatures are equal, and every tangent vector is a principal direction. The name "umbilic" comes from the Latin umbilicus - navel.Umbilic points generally occur as isolated points in the elliptical region of the surface; that is, where the Gaussian curvature is positive. For a surfaces with genus 0, e.g. an ellipsoid, there must be at least four umbilics, a consequence of the Poincaré–Hopf theorem.The sphere is the only surface with non-zero curvature where every point is umbilic. A flat umbilic is an umbilic with zero Gaussian curvature. The monkey saddle is an example of a surface with a flat umbilic and on the plane every point is a flat umbilic.The three main type of umbilic points are elliptical umbilics, parabolic umbilics and hyperbolic umbilics. Elliptical umbilics have the three ridge lines passing through the umbilic and hyperbolic umbilics have just one. Parabolic umbilics are a transitional case with two ridges one of which is singular. Other configurations are possible for transitional cases. These cases correspond to the D4-, D5 and D4+ elementary catastrophes of René Thom's catastrophe theory.Umbilics can also be characterised by the pattern of the principal direction vector field around the umbilic which typically form one of three configurations: star, lemon, and lemonstar (or monstar). The index of the vector field is either −½ (star) or ½ (lemon, monstar). Elliptical and parabolic umbilics always have the star pattern, whilst hyperbolic umbilics can be star, lemon, or monstar. This classification was first due to Darboux and the names come from Hannay.configurations of lines of curvature near umbilics".
- Umbilical_point thumbnail Lignes_de_courbure_ellipsoide.jpg?width=300.
- Umbilical_point wikiPageExternalLink NSF.htm.
- Umbilical_point wikiPageExternalLink text-idx?c=umhistmath;idno=ABV4153.0001.001.
- Umbilical_point wikiPageExternalLink text-idx?c=umhistmath;idno=ABV4153.0002.001.
- Umbilical_point wikiPageExternalLink text-idx?c=umhistmath;idno=ABV4153.0003.001.
- Umbilical_point wikiPageExternalLink text-idx?c=umhistmath;idno=ABV4153.0004.001.
- Umbilical_point wikiPageID "9757480".
- Umbilical_point wikiPageRevisionID "597310955".
- Umbilical_point hasPhotoCollection Umbilical_point.
- Umbilical_point subject Category:Differential_geometry_of_surfaces.
- Umbilical_point subject Category:Surfaces.
- Umbilical_point type Artifact100021939.
- Umbilical_point type Object100002684.
- Umbilical_point type PhysicalEntity100001930.
- Umbilical_point type Surface104362025.
- Umbilical_point type Surfaces.
- Umbilical_point type Whole100003553.
- Umbilical_point comment "In the differential geometry of surfaces in three dimensions, umbilics or umbilical points are points on a surface that are locally spherical. At such points the normal curvature in all directions are equal, hence, both principal curvatures are equal, and every tangent vector is a principal direction.".
- Umbilical_point label "Ombilic (surface)".
- Umbilical_point label "Umbilical point".
- Umbilical_point label "Точка округления".
- Umbilical_point sameAs Ombilic_(surface).
- Umbilical_point sameAs m.02pr81m.
- Umbilical_point sameAs Q3351935.
- Umbilical_point sameAs Q3351935.
- Umbilical_point sameAs Umbilical_point.
- Umbilical_point wasDerivedFrom Umbilical_point?oldid=597310955.
- Umbilical_point depiction Lignes_de_courbure_ellipsoide.jpg.
- Umbilical_point isPrimaryTopicOf Umbilical_point.
