Plücker formulas

Plücker formulas relate the geometric properties of a plane algebraic curve—such as its degree, the number of special points called cusps and nodes, and its inflection points. They establish mathematical relationships between these features, showing that the count of certain singularities and tangents is interconnected. Essentially, these formulas help mathematicians understand how the complex shape of a curve influences, and is influenced by, its tangent and intersection behaviors, revealing a deep harmony between the curve's topology and geometry.