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umbilic
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There are 7 letters in UMBILIC ( B3C3I1L1M3U1 )
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Definitions of umbilic in various dictionaries:
UMBILIC - In the differential geometry of surfaces in three dimensions, umbilics or umbilical points are points on a surface that are locally spherical. At suc...
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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 curvatures 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 surfaces with genus 0, e.g. an ellipsoid, there must be at least four umbilics, a consequence of the PoincaréHopf theorem. An ellipsoid of revolution has only two umbilics.* 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. A torus can have no umbilics, but every closed surface of no |