Welcome to my webpage Avalon !
In
this wabpage, I introduce you to my one of mathematical discocoveries,
which I found when I was a high school student. However, the
discoveries can be wrong, so please do not believe them too much.
By the way, my discoveries are about complex numbers. Thus, first, I tell you to a very important person and formula about my discoveries.
Do you know the below picture's person?
I think you may not know him. He is Leonhard Euler, some people call him the king of mathematics, like Karl Friedrich Gauss. It is difficult to decide who the king is because both Euler and Gauss were eminent geniuses in mathematics. Also, both of them had a great influence on mathematics, so to think who the king of mathematics is depends on a person. By the way, I will state about him briefly.
Euler was Swiss mathematician and physicist. He was born in near Basel, Swizerland, on April 15th, 1707, and his father was a churchman. The father wanted Euler to succeed to his job, but a famous mathematician persuaded him to permit Euler to be a mathematician. Thus, Euler managed to be one of the greatest mathematician. Euler left countless achievements for us, so if someone merely says "Tell me Euler's expression, please", it is impossible to recognize what Euler's expression is.
Next, I focuson Euler's formula. That is expressed as below.
By the way, my discoveries are about complex numbers. Thus, first, I tell you to a very important person and formula about my discoveries.
Do you know the below picture's person?
I think you may not know him. He is Leonhard Euler, some people call him the king of mathematics, like Karl Friedrich Gauss. It is difficult to decide who the king is because both Euler and Gauss were eminent geniuses in mathematics. Also, both of them had a great influence on mathematics, so to think who the king of mathematics is depends on a person. By the way, I will state about him briefly.
Euler was Swiss mathematician and physicist. He was born in near Basel, Swizerland, on April 15th, 1707, and his father was a churchman. The father wanted Euler to succeed to his job, but a famous mathematician persuaded him to permit Euler to be a mathematician. Thus, Euler managed to be one of the greatest mathematician. Euler left countless achievements for us, so if someone merely says "Tell me Euler's expression, please", it is impossible to recognize what Euler's expression is.
Next, I focuson Euler's formula. That is expressed as below.
In this case, e is a radix of natural logarithm, and the value is about 2.71828. i is imaginary unit, and, the definition is that 
. Also, 
is not a degree of angle, such as 
. The is radian, so is expressed like
is the circular constant, and in the circular measure, 
. In addition, the value of the
can be a complex number. By way of paranthesis, the importance of
this formula is to connect between trigonometric function and
exponential. Also, if is instituted for the formula, the expression is changed as below.
Next page, I will show you a part of my discoveries with using Euler's formula.
By the way, below links are very useful to understand what I stated and develop your knowledge of mathematics, so please use them if you do not understand what I showed you or are interested in mathematics
. Also, is not a degree of angle, such as . The is radian, so is expressed like is the circular constant, and in the circular measure, . In addition, the value of the
can be a complex number. By way of paranthesis, the importance of
this formula is to connect between trigonometric function and
exponential. Also, if is instituted for the formula, the expression is changed as below. | ||
| then, |  | |
 | ||
| thus, |  |
This expression 
is called the great treasure of humans.
That's because the expression has all important characters for mathematics, which are
is called the great treasure of humans.That's because the expression has all important characters for mathematics, which are
Next page, I will show you a part of my discoveries with using Euler's formula.
By the way, below links are very useful to understand what I stated and develop your knowledge of mathematics, so please use them if you do not understand what I showed you or are interested in mathematics
