Geometry of plane curves (Q545194)

The authors develop Plücker like formuluae for certain plane curves relating the number of same side and opposite side bitangencies with the number of double points and points of inflection. For that purpose they define a function \(F\) for a given curve such that it vanishes at double points, inflection points, and bitangencies. The close inspection of the function \(F\) and its index allows to prove the main result. In this way results of \textit{B. Halpern} [Bull. Am. Math. Soc. 76, 96--100 (1970; Zbl 0192.58502)] are extended.