(If clicked, it will be expanded.)
Autumnal tints of the ravine
on Shidokigawa rever
in Fukushima Pref., Japan
at the beginning of November in 1992
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☆ Thanks and donation to Wikipedia
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I Section of Science and Technology
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II Drawing a Figure with Mathematics
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(4) We Find an Equation of Egg Shaped Curves.
An equation of egg shaped curve, which resembles to the shape of the actual egg, is obtained.
The detail is here 
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(5)
Equation of Egg Shaped Curves 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 
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(6)
Equation of Egg Shaped Curves 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 
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(7)
Equation of Egg Shaped Curves 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 
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(8) Equation of Egg Shaped Curves V
Newly found equation of egg shaped curve is proposed.
The detail is here 
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(9) Equation of Egg Shaped Curves VI
We will treat a transformation of the equation from a convex circle into that of an egg shaped curve.
The detail is here 
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(10) Equation of Egg Shaped Curves 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
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(11) Equation of Heart Curves
 
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 
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(12) Heart Curves II
It is tried that a cardioid is reformed into a heart curve by two kinds of method.
The detail is here
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(13) Heart Curves 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 inverse-trigonometrical function
from that using the square root function.
The detail is here
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(14) Heart Curves III
Equation of heart curve is tried to be composed with the use of the exponential function.
The detail is here
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(15) 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
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(16)
Equations of Convex and Concave Circles
with the Use of Exponential Equation
The detail is here
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(17)
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
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(18) Graphics of Shape of a Flower II
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
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(19) Eye Shaped Curves
The detail is here
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(20)
Equation to Display a Shape of Rectangle with the Use of Exponential Function
The detail is here
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(21)
Napier's Number and Exponential Function
Napier's number 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 ultimate-value's expression of the Napier's number
and the analytic treatment of the exponential function.
The detail is here 
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(22)
A Solution Method of the 4th Order Equation ?
Apart from the ordinary method, a solution method of the 4th order equation which we have thought of is introduced.
The detail is here
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(23)
Equation of Curve Expressing Character S
Equation of curve expressing character S is tried to be composed with the use of the exponential function.
The detail is here
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(24)
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
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(25) 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
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(26) 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
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(27) 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
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III Leisure and Strange Matter
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(28) Akiko's Overseas Travels
28.1 Akiko's Overseas Travels I
The detail is here
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28.2 Akiko's Overseas Travels II
The detail is here
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28.3 Akiko's Overseas Travels III
The detail is here
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28.4 Akiko's Overseas Travels IV
The detail is here
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28.5 Akiko's Overseas Travels V
The detail is here
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28.6 Akiko's Overseas Travels VI
The detail is here
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(29) Slightly Rare Nature-View
29.1 Parhelion !
In August of 1991, we encounters the phenomenon of parhelion in the evening at Naka city, Ibaraki prefecture in Japan.
The detail is here
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29.2
Cloud with Clear Outline
In Sep. 23 (Sun.), 1990, the left picture was taken at a parking lot (2700 meters of altitude) of Mt. Norikura (3025.6 meters of altitude) in Japan.
View of the parking area taken after this cloud has left the immediateness for the left side slowly is shown in the lower right.
The detail is here
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29.3 These are snow clouds.
In Oct. 23, 1994, the left pictures of snow clouds were taken at Shibu mountain pass (2152 meters of altitude) in Nagano pref. in Japan.
The detail is here
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29.4
Foot of a Rainbow (At a Rainbow Bridge)
We encountered the foot of a rainbow at Kitsuregawa, Sakura city, Tochigi Pref. Japan
by the influence of slow typhoon No. 12 in Sep. 3rd (Sat.) in 2011.
The detail is here
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29.5
Black Clouds
When we drove a car on Rt. 18 in Annaka city, Gumma Pref. in Japan towards Nagano,
we came occasionally under big black clouds at 16:00, Sep. 23 (Fri.), 2011.
The detail is here
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29.6
Large Hail Has Fallen
Large hail has fallen in Hitachinaka city of Ibaraki prefecture in Japan, an hour after Tsukuba city
of the same prefecture was seized with a tornado in May 6th, 2012.
The detail is here
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(30) Solid Picture ?
A pair of pictures, which are used for left eye and for the right eye respectively, are prepared as like as used in a usual solid picture.
The respective pictures are cut on the slit lengthwise and the respective pictures for the left and the right are pasted together alternately.
In this simple way, a solid picture (?) is thynthesized.
The detail is here
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(31) Color Code
Starting from the three primalies, color code is shown clearly.
The detail is here
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(If clicked, it will be expanded.)
Azuma-kofuji volcano
in Bandai-Azuma National Park
in Fukushima Pref., Japan
on August 8th in 2010
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This sentence is here to reserve a margin in this table.
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