The ampersand curve is the name given by Cundy and Rowlett (1989, p. 72) to
the quartic curve with implicit equation
(1)
Although it is not mentioned by Cundy and Rowlett, this curve is significant because it is the original example (after subtracting a small positive constant ) of a quartic curve having 28 real bitangents
constructed by Plücker (Plücker 1839, Gray 1982).
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 72, 1989.Gray,
J. "From the History of a Simple Group." Math. Intell.4,
59-67, 1982. Reprinted in The
Eightfold Way: The Beauty of the Klein Quartic (Ed. S. Levy). New York:
Cambridge University Press, pp. 115-131, 1999.Plücker, J.
Theorie der algebraischen Curven: Gegründet auf eine neue Behandlungsweise
der analytischen Geometrie. Berlin: Adolph Marcus, 1839.Sloane,
N. J. A. Sequences A101801 and A101802 in "The On-Line Encyclopedia of Integer
Sequences."
) of a quartic curve having 28 real bitangents
constructed by Plücker (Plücker 1839, Gray 1982).
, 
, and 
.
, 
,
and 
.
The vertical asymptotes are at 
and 
![r^2[2cos(2theta)+cos(4theta)+9]-r[37costheta+5cos(3theta)]
+[22cos(2theta)+16]=0.](/images/equations/AmpersandCurve/NumberedEquation2.svg)
