In geometry, the ampersand curve is a type of quartic plane curve. It was named after its resemblance to the ampersand symbol by Henry Cundy and Arthur Rollett.
The ampersand curve is the graph of the equation
formula_1
The graph of the ampersand curve has three crunode points where it intersects itself at (0,0), (1,1), and (1,-1). The curve has a genus of 0.
The curve was originally constructed by Julius Plücker as a quartic plane curve that has 28 real bitangents, the maximum possible for bitangents of a quartic.
It is the special case of the Plücker quartic
formula_2
with formula_3
The curve has 6 real horizontal tangents at
And 4 real vertical tangents at formula_7 and formula_8
It is an example of a curve that has no value of x in its domain with only one y value.