Cayley–Bacharach Formulas

Cayley–Bacharach Formulas

The Cayley–Bacharach theorem states that all cubic curves through eight given points in the plane also pass through a unique ninth point. We write that point as an explicit rational function in the other eight.

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Bibliographische Detailangaben
Veröffentlicht in:The American mathematical monthly 2015-11, Vol.122 (9), p.845-854
Hauptverfasser: Ren, Qingchun, Richter-Gebert, Jürgen, Sturmfels, Bernd
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Computer algebra systems
Conic sections
Coordinate systems
Geometric planes
Geometry
Mathematical analysis
Mathematical functions
Mathematical theorems
Polynomials
Polytopes
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Beschreibung
Zusammenfassung:The Cayley–Bacharach theorem states that all cubic curves through eight given points in the plane also pass through a unique ninth point. We write that point as an explicit rational function in the other eight.
ISSN:0002-9890
1930-0972
DOI:10.4169/amer.math.monthly.122.9.845