A bitangent is a line that is tangent to a curve at two distinct points.
There exist plane quartic curves
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that have 28 real bitangents (Shioda 1995, Trott 1997), for example
(Trott 1997), illustrated above.
SEE ALSO: Bitangent Vector, Klein's equation , Plücker Characteristics, Secant Line, Solomon's Seal Lines, Tangent Line
REFERENCES:
Frame, J. S. "The Classes and Representations of the Groups of 27 Lines and 28 Bitangents." Ann. Mat. Pura Appl. 32, 83-119, 1951.
Shioda, T. "Weierstrass Transformations and Cubic Surfaces." Comm. Math. Univ. Sancti Pauli 44, 109-128, 1995.
Trott, M. "Applying GroebnerBasis to Three Problems in Geometry." Mathematica Educ. Res. 6, 15-28, 1997.
