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- Q4455043 subject Q6482584.
- Q4455043 subject Q8851964.
- Q4455043 subject Q8851987.
- Q4455043 abstract "In mathematics, the Cayley–Bacharach theorem is a statement about cubic curves (plane curves of degree three) in the projective plane P2 The original form states:Assume that two cubics C1 and C2 in the projective plane meet in nine (different) points, as they do in general over an algebraically closed field. Then every cubic that passes through any eight of the points also passes through the ninth point.A more intrinsic form of the Cayley–Bacharach theorem reads as follows:Every cubic curve C1 on an algebraically closed field that passes through a given set of eight points P1, ..., P8 also passes through a certain (fixed) ninth point P9, counting multiplicities.A related result on conics was first proved by the French geometer Michel Chasles and later generalized to cubics by Arthur Cayley and Isaak Bacharach (1886).".
- Q4455043 thumbnail 9-points_theorem.png?width=300.
- Q4455043 wikiPageExternalLink 0508076.
- Q4455043 wikiPageExternalLink S0273-0979-96-00666-0.pdf.
- Q4455043 wikiPageWikiLink Q1047547.
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- Q4455043 wikiPageWikiLink Q493171.
- Q4455043 wikiPageWikiLink Q5456251.
- Q4455043 wikiPageWikiLink Q591310.
- Q4455043 wikiPageWikiLink Q6482584.
- Q4455043 wikiPageWikiLink Q703577.
- Q4455043 wikiPageWikiLink Q7333126.
- Q4455043 wikiPageWikiLink Q736753.
- Q4455043 wikiPageWikiLink Q851166.
- Q4455043 wikiPageWikiLink Q8851964.
- Q4455043 wikiPageWikiLink Q8851987.
- Q4455043 wikiPageWikiLink Q899002.
- Q4455043 wikiPageWikiLink Q929302.
- Q4455043 comment "In mathematics, the Cayley–Bacharach theorem is a statement about cubic curves (plane curves of degree three) in the projective plane P2 The original form states:Assume that two cubics C1 and C2 in the projective plane meet in nine (different) points, as they do in general over an algebraically closed field.".
- Q4455043 label "Cayley–Bacharach theorem".
- Q4455043 depiction 9-points_theorem.png.