The Yamamoto egg is an egg-shaped oval defined, for parameters 
, by the quartic
curve
 |
(1)
|
It is a reflected single Kepler's folium, expressed in a convention used for egg-shaped curves (Yamamoto 2007, Chan et al. 2018). Its polar equation is
 |
(2)
|
for 
. This follows from the usual Kepler's folium with parameters 
and 
, followed by reflection
in the 
-axis.
Yamamoto (2007) gives the parametric equations
 |  |  |
(3)
|
 |  |  |
(4)
|
where 
. For 
, the real oval is
smooth even though the corresponding algebraic curve
has a singular point at the origin.
The limit 
is a circle with center 
and radius 
. At 
, the origin
becomes a cusp.
Green's theorem gives the enclosed area
 |
(5)
|
