Googling for " plane curves " yields some interesting galleries, but not what I'm looking for . ~ talk ) 22 : 43, 24 May 2010 ( UTC)
42.
The anticanonical divisor is not very ample, and its linear system defines a map from the del Pezzo surface to the projective plane, branched over a quartic plane curve.
43.
Since the real number field is not algebraically closed, the geometry of even a plane curve " C " in the real projective plane is not a very easy topic.
44.
The name comes from a duality property of singular plane curves studied by ( who was fond of claiming that he did not understand the definition of a Gorenstein ring ).
45.
One of the challenging problems of real algebraic geometry is the unsolved Hilbert's sixteenth problem : Decide which respective positions are possible for the ovals of a nonsingular plane curve of degree 8.
46.
Salmon also published two other mathematics texts, " A Treatise on Higher Plane Curves " ( 1852 ) and " A Treatise on the Analytic Geometry of Three Dimensions " ( 1862 ).
47.
A simple case of this is for a hypersurface ( a codimension 1 subvariety, the zeros of a single polynomial, the case m = n-1 ), of which plane curves are an example.
48.
More generally, for an arbitrary closed curve in space the average curvature is \ ge \ frac { 2 \ pi } { P } with equality holding only for convex plane curves.
49.
An inflection point of a plane curve is a point where the curve has at least three point contact with its tangent line, e . g . the point ( 0, 0 ) on the curve.
50.
First, the conjugate relationship between tangent points and tangent lines can be generalized to reducible ) case of a quartic plane curve, and the external and internal tangent lines are the bitangents to this quartic curve.
