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- Focal_surface abstract "For a surface in three dimension the focal surface, surface of centers or evolute is formed by taking the centers of the curvature spheres, which are the tangential spheres whose radii are the reciprocals of one of the principal curvatures at the point of tangency. Equivalently it is the surface formed by the centers of the circles which osculate the curvature lines. As the principal curvatures are the eigenvalues of the second fundamental form, there are two at each point, and these give rise to two points of the focal surface on each normal direction to the surface. Away from umbilical points, these two points of the focal surface are distinct; at umbilical points the two sheets come together. When the surface has a ridge the focal surface has a cuspidal edge, three such edges pass through an elliptical umbilic and only one through a hyperbolic umbilic. At points where the Gaussian curvature is zero, one sheet of the focal surface will have a point at infinity corresponding to the zero principal curvature.".
- Focal_surface thumbnail Focal_surface.png?width=300.
- Focal_surface wikiPageID "9789196".
- Focal_surface wikiPageRevisionID "578963928".
- Focal_surface hasPhotoCollection Focal_surface.
- Focal_surface subject Category:Surfaces.
- Focal_surface type Artifact100021939.
- Focal_surface type Object100002684.
- Focal_surface type PhysicalEntity100001930.
- Focal_surface type Surface104362025.
- Focal_surface type Surfaces.
- Focal_surface type Whole100003553.
- Focal_surface comment "For a surface in three dimension the focal surface, surface of centers or evolute is formed by taking the centers of the curvature spheres, which are the tangential spheres whose radii are the reciprocals of one of the principal curvatures at the point of tangency. Equivalently it is the surface formed by the centers of the circles which osculate the curvature lines.".
- Focal_surface label "Focal surface".
- Focal_surface sameAs m.02ps7wx.
- Focal_surface sameAs Q5463861.
- Focal_surface sameAs Q5463861.
- Focal_surface sameAs Focal_surface.
- Focal_surface wasDerivedFrom Focal_surface?oldid=578963928.
- Focal_surface depiction Focal_surface.png.
- Focal_surface isPrimaryTopicOf Focal_surface.
