## Invariants of curves

Sun 15 Sep 2013Plane curves of 2. order (conic sections) treated by their invariants.

The article Invariants of curves of second order treats conic sections as algebraic curves by their invariants.

Determining the invariants of curves of second order

a_{11}x^{2} +2a_{12}xy + a_{22}y^{2} + 2_{13}x +2a_{23}y + a_{33} = 0

from the coefficients $a_{ik}$ of the equation is a well known task.

We derive formulas for the invariants following an elementary high school

course developed by Freudenthal and Heinrich 50 years ago.