The curve in the case that a=1 and c=2.9 gives the closest shape to an actual egg.
The comparison between the curve in this case and the shape of an actual egg is shown in Fig.5.
Fig.5 Comparison between the egg shaped curve
in the case that a=1 and c=2.9 (pink colored curve)
and the shape of an actual egg
In the last, Eq.(1) may be transformed into Eq.(2).
In purpose to calculate the numerical coordinates data of five species of curves as shown in Figs.1 to 3, a C++ program originated from Eq. (1)
is given by
Another C++ program treating a single curve is given by
In the latter program, the constants are settled as =1, and =0.29.
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.