In mathematics, the Cayley–Bacharach theorem is a statement about cubic curves (plane curves of degree three) in the projective plane P2. The original...

coniques. Par B. P." Pascal's theorem is a special case of the Cayley–Bacharach theorem. A degenerate case of Pascal's theorem (four points) is interesting;...

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case of the Cayley–Bacharach theorem. The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus's theorem, with each...

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Isaak Bacharach (2 December 1854 – 22 September 1942) was a German mathematics professor in Erlangen who proved the Cayley–Bacharach theorem on intersections...

Cayley–Bacharach theorem (projective geometry) Ceva's theorem (geometry) Clifford's circle theorems (Euclidean plane geometry) Commandino's theorem (geometry)...

cubics does, and the points satisfy additional properties; see Cayley–Bacharach theorem. A cubic curve may have a singular point, in which case it has...

position, and indeed satisfy an addition constraint, as stated in the Cayley–Bacharach theorem. Four points do not determine a conic, but rather a pencil, the...

theory can be used to answer the question of the completeness. The Cayley–Bacharach theorem is a property of a pencil of cubics, which states that the base...

MR 1011763. Eisenbud, David; Green, Mark; Harris, Joe (1996). "Cayley-Bacharach theorems and conjectures". Bull. Amer. Math. Soc. New Series. 33 (3): 295–324...

and accordingly satisfy an additional constraint, namely the Cayley–Bacharach theorem that any cubic that contains eight of the points necessarily contains...

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