Bézout's theorem
Teorema de Bézout
- Date
- 1779 · confidence medium
- Place
- Paris, France
- Credited to
- Étienne Bézout
- Field
- Knowledge & symbols
What was discovered
An algebraic-geometry theorem fixing the number of common points of algebraic curves or hypersurfaces: two plane curves without a common component of degrees d1 and d2 meet in d1×d2 points, counted with multiplicity and including those at infinity or with complex coordinates.
What it led to
- the foundation of intersection counting in algebraic geometry
- generalization to projective hypersurfaces in n variables
- a standard tool in enumerative geometry
- theoretical basis of numerical methods for solving polynomial systems