What is the origin of the natural constant e in mathematics?

The natural constant e is lim (1+ 1/x) x, x->; +∞ or lim (1+z) (1/z), z-> 0, whose value is about 2.7 1828, is an infinite acyclic number.

Euler formula of natural logarithm base

(approximately equal to the base of natural logarithm 2.7 1828-E)

Euler is known as Shakespeare in the digital world. He is the most prolific mathematician in history and a scholar who has written the most books in various fields (including all branches of mathematics and mechanics, optics, acoustics, water conservancy, astronomy, chemistry, medicine and other theories and applications). ). In the history of mathematics,18th century is called "Euler era".

Euler was born in Switzerland. At the age of 365,438+0, he lost his right eye vision and was blind at the age of 59. But he is optimistic, and his memory and concentration are amazing, which enables him to think complex problems accurately in the noisy environment of 13 children.

Euler was humble all his life and never named his discovery after himself. Only the base of natural logarithm, which is about 2.7 1828, was named E by him. However, due to his extensive contributions to mathematics, important constants, formulas and theorems named after him can often be seen in many branches of mathematics.

Many mathematical symbols that we are used to now were invented and introduced by Euler, such as function symbols f(x), π, e, ∑, logx, sinx, cosx, imaginary number I and so on. High school teachers often use a joke about the base e of natural logarithm to help students remember a very special differential formula: in a mental hospital, a patient says to others all day, "I differentiate you, I differentiate you." I don't know why, these patients all have simple calculus concepts. 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."

This differential formula is: No matter how many times E differentiates X, the result is still E! No wonder math students use e to describe unswerving love!

Compared with π being the first letter of a circle in Greek, the origin of E is less known. Some people even think that Euler takes the first letter of his name as the natural logarithm.

Euler chose e for two reasons: first, after the four letters A, B, C and D that are commonly used, the first letter that is not often used is e, so he naturally chose this symbol, which represents the base of natural logarithm; One is that e is the first letter of the index. Although you may suspect that the native language of Swiss Euler is not English, it is actually an index in French and German.