Steiner's conic problem asks how many nonsingular conic sections in the complex projective plane
are tangent to five given nonsingular conic
sections chosen sufficiently generally. The answer is 3264 (Eisenbud and Harris
2016, Breiding et al. 2020).
Here sufficiently general means that the choice belongs to a suitable nonempty open set in the Zariski
topology on the space of 5-tuples of conic
sections (Eisenbud and Harris 2016). The count is over the complex
numbers and does not require the conic sections
to have real coefficients .
See also Complex Projective Plane ,
Conic Section ,
Enumerative
Geometry ,
Tangency
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References Breiding, P.; Sturmfels, B.; and Timme, S. "3264 Conics in a Second." Notices Amer. Math. Soc. 67 , 30-37, 2020. https://doi.org/10.1090/noti2010 . Eisenbud,
D. and Harris, J. 3264 and All That: A Second Course in Algebraic Geometry.
Cambridge, England: Cambridge University Press, 2016. https://doi.org/10.1017/CBO9781139062046 . Numberphile.
"The Journey to 3264." Apr. 2, 2023. https://www.youtube.com/watch?v=NWahomDHaDs .
Cite this as:
Weisstein, Eric W. "Steiner's Conic Problem."
From MathWorld https://mathworld.wolfram.com/SteinersConicProblem.html
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