They say the most beautiful equation for mankind is as follows:
e**(i *π) = -1
i = root(-1) = (-1)**(1/2): a unit imaginary number;
e = the natural (Napierian) logarithm, or 2.7182818…;
π (or pi) = the circular constant, or 3.14159265…
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You may wonder what kinds of numbers are used in the most advanced mathematics and science. They use only four types of numbers: ordinary numbers (composed of basic numbers from 0 to 9), π, “e,” and “i.”
Even today, almost all the scientific and engineering documents can be read and understood, if you know the above four types of numbers.
The equation, e**(i *π) = -1, includes the all types of the numbers. Therefore, they say it is the most beautiful equation, or a miracle equation.
However, it is a direct result of Euler's formula:
e**(i * x) = cos(x) + i*sin(x), with x = π, and cos(π) = -1 and sin (π) = 0.
On the other hand, Euler's formula is a result of the following expansions:
cos (x) = Sum of [(-1)**k]*(x**2k) / [(2k)!] from k =0 to ∞;
sin (x) = Sum of [(-1)**k]*[x**(2k-1)] / [(2k-1)!] from k =0 to ∞; and
e**x = Sum of x**k / k! from k =0 to ∞
while k! = 1*2*3*…*(k-1)*k.
(Here if x = ix,
However, the key to the expansions is as follows:
d cos(x) / dx = -sin(x);
d sin(x) / dx = cos(x); and
d e**x /dx = e**x
while d/dx means differential by x.
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The nature can be expressed and analyzed by differential equations. Thus what makes possible the most beautiful equation is definitions of the functions of e**x, cos (x), and sin (x) based on each differential equation.
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It can apply to human beings. If a woman called a beauty ever exists, which Jesus Christ never assures us of, we can test her by differentiating her features. But, human differentiation might not be so simple as the above mathematical ones.
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But, as for me, the equation, e**(i *π) = -1, does not seem to be the most beautiful equation. The key differentials do not look like so, either.
Right from the start, mathematics and numbers are tools, operations, processes, and methods. They can be nice or rational, but “beautiful” is too much.
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If a woman loves God or Jesus Christ, her internal structure should be rearranged by love and faith so as to be able to respond to outer force, including men’s observation, in a well differentiated manner. Consequently, she should look beautiful in safety and security.
Otherwise, women should put on a veil. (Today, an eclipse happened on some part of the earth, mostly Islamic regions, symbolizing something.)
“IN THIS POWERFUL WAY, THE WORD OF THE LORD IS SPREADING”