
Fig.3 The second type of egg shaped curves

2. The second type of equation
Another one of two novel types of the equations expressing egg shaped curve proposed by Mr. Yasuyuki ASAI is written in the following;
. (3)
If we calculate Eq.(3) as varying the several values of b with the use of computer, we obtain Fig.3.
Thus, we may find egg shaped curves as seen in Fig.3.
Comparison between the curve in the case that a=1.35, b=0.9 and c=0.5 and the shape of an actual egg is shown in Fig.4. As seen in Fig.4, the egg shaped curve may approximately coincide to the shape of an actual egg.
Fig.4 Comparison between the egg shaped curve
in the case that a=1.35, b=0.9 and c=0.5 (pink colored curve) and the shape of an actual egg

In purpose to calculate the numerical coordinates data of five species of curves as shown in Fig.1, a C++ program originated from Eq. (1) is given by . Another C++ program treating a single curve 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 devided 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.

3. A conventional method to connect two ellipsoids into an egg shaped curve

Fig.5 Egg shaped curves into the each of which two ellipsoids are connected

A simple method to connect two ellipsoids into an egg shaped curve is also proposed by Mr. Yasuyuki ASAI. The equation for expressing such an egg shaped curve is written in the following;
. (4)
In this equation, sgn(x) is defined as
. (5)
In the case of c=a, Eq.(4) gives an ellipsoid.
If we calculate Eq.(4) as varying the several values of c with the use of computer, we obtain Fig.5.
Comparison between the curve in the case that a=1, b=0.72 and c=0.9 and the shape of an actual egg is shown in Fig.6. As seen in Fig.6, the egg shaped curve may approximately coincide to the shape of an actual egg.
Fig.6 Comparison between the egg shaped curve
in the case that a=1, b=0.72 and c=0.9 (pink colored curve) and the shape of an actual egg

In purpose to calculate the numerical coordinates data of five species of curves as shown in Fig.5, a C++ program originated from Eq. (4) is given by . Another C++ program treating a single curve is given by . By executing thte either C++ program, a common text file named "egg_shaped_curve.txt" including the calculated data is produced. Each interval of these data is devided 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.

