The ampersand curve is the name given by Cundy and Rowlett (1989, p. 72) to the quartic curve with implicit equation
(1)
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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), namely Plücker's quartic.
The ampersand curve has crunodes at , , and .
The horizontal asymptotes are at , , and . The vertical asymptotes are at and
The polar equation is given by solving the quadratic equation
(2)
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The area enclosed by the ampersand is given approximately by
(3)
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(OEIS A101801) and the perimeter approximately by
(4)
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(OEIS A101802).