Dual Curves

 

ABSTRACT: We have shown that curves in projective space can be classified by
simple change of variables. Though not a classification, we can group a curve
in another way - by introducing its dual curve. Dual projective curves take the
tangents of a curve in projective space and map these tangent lines to points.
When this is done, we notice some interesting properties of the dual curve. For
example, we note that each curve has a unique dual curve and that when you take
dual of a dual curve, you return to the original curve. In my presentation, I
will introduce this dual curve and show ways of calculating it, as well as
other interesting properties of the dual curve and its pair.