Title: 2 7 1 8 2 8 1 8 _ _

One day, my daughter, who was still in primary school, gave me a math problem. She asked me to find out the rules and fill in the numbers in the blanks.

Fortunately, out of admiration for LeonhardEuler, Euler's figures are impressive, otherwise it would be a shame to be defeated by primary school students.

You are right. The answer to this question is Euler number E, which was first named by Euler.

E is sometimes called a natural constant, and the logarithm based on e is called a natural logarithm. (Von Neumann, a genius who passed Grade 8 before Zhu Ba, was the first to calculate E to 20 10 at 1949. )

There used to be a joke about e: in a mental hospital, a patient said to others all day, "I divide you, I divide you." For some reason, these patients all have a simple concept of calculus. They always think that one day they will be differentiated into zero and disappear like ordinary polynomial functions, so they avoid him. One day, however, he met an unmoved person. He was surprised. This person simply said to him, "I am the x power of E."

How natural is this natural constant e? First of all, this number is closely related to your wallet.

Suppose you deposit 1 yuan in the bank with interest of 100%. You will get (1+100%)1= 2 after one year.

Now, in order to absorb deposits, banks pay interest every six months, so the income after one year is (1+50%) 2 = 2.25.

Due to the economic depression, the competition between banks is too fierce. If monthly interest settlement is introduced and the interest is rolled, the income after one year will be (1+112)12 = 2.61times.

But at this time, the P2P platform was born, saying that it is nothing to pay interest every month. I will give you interest every minute, or even a shorter time to roll interest. Do you think it will develop?

That is to say, if n becomes infinite, will (1+ 1/n) n also become infinite?

Have you thought about it? Actually, this question is not that simple. At that time, a great mathematician Jacob Bernoulli tried to solve this problem, but there was no solution. It was not until 50 years later that Euler finally got the result.

It turns out that even if P2P can make you profitable all the time, you will not be developed, and this limit is Euler number E. When n becomes infinite, the limit value of (1+ 1/n) n is e.

See, this natural constant E sets a limit on deposits, and reminds all diaosi that you can never make a fortune by interest, especially those nonsense P2P.

Simply put, Euler number e is the limit of growth. Because of Euler number, all growth has a ceiling, which is everywhere in our life, including the growth of compound interest, the cooling of objects, the reproduction of cells and the decay of radioactive elements. ...

We call Euler number E and its transformation and synthesis form "natural law", and E is a quantitative expression of "natural law". The image expression of "natural law" is a spiral. Spirals are everywhere in nature, from galaxies and typhoons to flowers and shells to your fingerprints, hairpins, inner ears and nucleic acid structures ... The universe is full of spirals.

"Natural law" has inexhaustible aesthetic connotation, because it comes from extensive and profound nature.

Euler number e fully embodies the most essential thing of the formation, development and decline of the universe.

Pi π = 3.141592 65358979 ... You probably learned it in the third grade of primary school.

The most perfect plane symmetrical figure in the world is a circle, and a value obtained by dividing the circumference by the diameter is proved to be irrational. And this symbol π is also the first symbol that Euler decided to use and popularize.

It was Archimedes of Greece (about 240 BC) who first got π≈3. 14.

The Greek Ptolemy (about 150 BC) was the first to give the exact value of the last four digits of π decimal.

It was Zu Chongzhi of China (about 480) who first worked out the exact value of the last seven digits of π decimal.

This result was not rediscovered by German Otto and Dutch Antuoni until16th century. So China's calculation of pi is one thousand years ahead of the world.

So we are too familiar with pi, which is a heritage that China people have always been proud of.

π and Euler number e are irrational numbers and the most famous transcendental numbers.

The square of the imaginary number is negative 1. You will probably study in high school.

The imaginary unit "I" was also initiated by Euler.

We call a+bi (both a and b are real numbers) a complex number. Stewart believes that "... without this formula, many modern technologies such as electric lights and digital cameras could not have been invented." "

With the development of imaginary number, it has become a branch of mathematics-complex analysis. Engineers can use complex analysis to process data. Scientists extend calculus to complex numbers and get "complex variable function", which is very important for understanding electrical systems and many modern mathematical processing algorithms.

Imaginary numbers are widely used in electrical engineering, signal processing and mathematical theory.

Ok, now that we have π, E and I, will there be a relationship between them?

Euler unified our seemingly unrelated natural basis, pi and imaginary number in one formula:

This most beautiful and concise formula is named after him and is called Euler formula.

In physics, Euler's formula has a great influence, which relates circular motion, simple harmonic vibration, mechanical wave, electromagnetic wave and probability wave in physics. ......

Nobel Prize winner richard feynman called Euler's formula "our treasure" and "the most extraordinary formula in mathematics".

C.F.Gauss, a talented German mathematician, once said, "A person who sees this formula for the first time without feeling its charm will never become a first-class mathematician. 」

Mathematicians evaluate it as "a formula created by God, which we can only look at but can't fully understand".

So this formula is widely called the divine formula.

Of the crystallization formulas of human knowledge through the ages, only Euler formula is called God formula. What a breakthrough this is.

There is a famous anecdote, of course, some people regard it as a legend. In a court in the court of Catherine II, in front of the Russian Queen, Euler argued with the famous atheist philosopher Denis Diderot, who compiled the French encyclopedia and claimed that he knew everything. Euler only asked a sentence in a tone close to perfect faith:

Although Diderot also knew some mathematics, he didn't know how to deal with God's formula at all. He froze on the spot and burst into laughter like pearls. Feeling humiliated and angry, Diderot asked to leave Russia, which was generously approved.

Will anyone appreciate the beauty of mathematics in this era? No matter how beautiful this formula is, can I afford a house?

Euler should be glad that he was born in a great era. As soon as the formula came out, many awesome people applauded him. If in this day and age, will there be no one who even takes a look?

In many cases, history seems to be an infinite and acyclic decimal-irrational number. Those who once or now can control history, seemingly beyond, but unreasonable, will be eliminated before God's formula.

This is the most magical power of God's formula.