return

(5) Equation of Egg Shaped Curve II
Novel type expression of egg shaped curves has been proposed by Mr. ITOU, and contributed to this page in March, 2008.
The detail is here .
return

(6) Equation of Egg Shaped Curve III
Mr. Yasuyuki ASAI has informed another novel type of the equation expressing the egg shaped curve to Yamamoto in July, 2009. Under the informed equation, numerical calculations are performed by YAMAMOTO.
The detail is here .
return

(7) Equation of Egg Shaped Curve IV Mr. Yasuyuki ASAI has informed the other novel types of the equations expressing the egg shaped curve to Yamamoto in July, 2009. Under the informed equation, numerical calculations are performed by YAMAMOTO.
The detail is here .
return

return

(9) Equation of Egg Shaped Curve VI
We will treat a transformation of the equation from a convex circle into that of an egg shaped curve. The detail is here .
return

(10) Equation of Egg Shaped Curve VII
Mr. Yasuyuki ASAI has informed the more novel type of the equation expressing the egg shaped curve to Yamamoto in April, 2011.
The detail is here .
return

return

(12) Equation of Heart Curve
Heart curves are tried to be drawn by two kinds of simple calculation. The most simple way is thought to be that the each part of a circle is pulled up by some rate into a heart curve.
The detail is here .
return

(13) Heart Curve II
It is tried that a cardioid is reformed into a heart curve by two kinds of method.
The detail is here .
return

(14) Heart Curve II b
It is tried that a Cardioid is reformed into a heart curve as samely as in the section 3 of the previous page of Heart Curve II in the manner that the conversion equation of Eq.(9) in the previous page of Heart Curve II is displaced to the equation using inversetrigonometrical function from that using the square root function.
The detail is here .
return

(15) Heart Curve III
Equation of heart curve is tried to be composed with the use of the exponential function.
The detail is here .
return

(16) Spade Curve
We find only a heart curve, which may be adopted as the shape of a spade after the top and the bottom of the heart curve were made reverse, among a lot of the obtained heart curves.
The detail is here .
return

return

(18) Equation Expressing Star or Flower Graphics
On the base of "Equation of Concave Circle" introduced in the above column, we have tried to derive the equation expressing an asteroid or shape of a flower.
The detail is here .
return

(19) Flower Graphics
We try to produce shape of flower by calculation with the use of computer as an application of "heart curves II" introduced in the above column.
The detail is here .
return

return

return

(22) Napier's Constant and Exponential Function Napier's constant performs the main role expressing linear natural phenomena. The reason stands on the caracteristics that the derivative of exponential function is the exponential one itself. In this page, we intend that some foundation of its reason is made clear in respect to both the algebraic ultimatevalue's expression of the Napier's constant and the analytic treatment of the exponential function.
The detail is here .
return

return

return

(25) A Simple Simulation of Seashore Wave
To solve the form of seashore wave in hydrodynamic system is very difficult for the reason of a strong nonlinearity. Although the scientific acuracy is not expected, we try to simulate the form under simple assumption in this treatise.
The detail is here .
return

(26) Apple Shaped Curve
When a Cardioid is deformed into another figure with introducing some exponential functions, an apple shaped curve is found accidentally.
The detail is here .
return

(27) 3D Displays of Egg and Apple
The request is informed from Mr. Svein Daniel Solvenus to Yamamoto in 2011 how we can make 3D display of an egg with the use of the equations described in the above sections (4) and (5).
The detail is here .
return

(28) 3D Display of Spirals on an Egg and an Apple
I received from Mr. Joshua Gottdenker the message in 2011 that he wants to make a model of shape similar to the spherical spiral onto an egg instead of a sphere.
The detail is here .
return
