View source for Flat point

A point on regular surface at which the osculating paraboloid degenerates to a plane. At a flat point the Dupin indicatrix is not defined, the Gaussian curvature is equal to zero and the second fundamental form and all remaining curvatures are also equal to zero.

A point at which the torsion of a curve vanishes is called a flat point of the spatial curve.



====Comments====
A flat point is sometimes called a planar point. The terminology of course derives from the curvature zero property.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  C.C. Hsiung,   "A first course in differential geometry" , Wiley  (1981)  pp. Chapt. 3, Sect. 4</TD></TR></table>