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.
A flat point is sometimes called a planar point. The terminology of course derives from the curvature zero property.
|[a1]||C.C. Hsiung, "A first course in differential geometry" , Wiley (1981) pp. Chapt. 3, Sect. 4|
Flat point. D.D. Sokolov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Flat_point&oldid=14781