Comparison between the curve in the case that a=0, b=2.0, c=2.65 and d=k1=k2=k3=1 and the shape of an actual egg is shown in Fig.4, where the value of the parameter c is a little changed from that in Fig.1. As seen in Fig.4, the egg shaped curve made from the equation of the concave distorted circle may approximately coincide to the shape of an actual egg.

Fig.4 Comparison between the egg shaped curve in
the case that a=0, b=2.0, c=2.65 and d=k1=k2=k3=1
(pink colored curve) and the shape of an actual egg

In purpose to calculate the numerical coordinates data of a single curve as shown in Figs.1, 2 and 3, a C++ program originated from Eq.(2) is given by .
By executing the either C++ program, a common text file named "egg_shaped_curve.txt" including the calculated data is produced. Each interval of these data is divided by 'comma'. After moving these calculated data into an Excel file, we obtain an egg shaped curve with the use of a graph wizard attached on the Excel file.

In the next, the transformation of the equation from the convex circle to an egg shaped curve leads to
. (4)
If we solve Eq.(4), the following equation is derived.
.
(5)
The condition that Eq.(5) exists is
.
(6)
When we pursuit the nearest shape to an actual egg as calculating Eq.(5) with the use of computer, it is recognized that the egg shaped curves are found in the wide range of parameters. Three cases of , and the other one are displayed with the blue colored curves in Figs.5, 6 and 7 respectively. The pink colored curves in these figures indicate the previously found egg shaped curve as a reference.
It must be paid attention to that Eq.(4) itself is invalid as when .
