The quartic curve with implicit equation
 |
(1)
|
It 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
![r^2[2cos(2theta)+cos(4theta)+9]-r[37costheta+5cos(3theta)] +[22cos(2theta)+16]=0.](http://mathworld.wolfram.com/images/equations/AmpersandCurve/NumberedEquation2.gif) |
(2)
|
The area enclosed by the ampersand is given approximately by
 |
(3)
|
(Sloane's A101801) and the perimeter approximately by
 |
(4)
|
(Sloane's A101802).
REFERENCES:
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 72, 1989.
Sloane, N. J. A. Sequences A101801 and A101802 in "The On-Line Encyclopedia of Integer Sequences."
