Its numerical value is about (decimal point 100): e ≈ 2.7182818284 59045 23536 02874 71352 66249 77572 47093 6995 95749 66966.
The constant e was first developed by John? 16/kloc-a table in the appendix of napier's logarithmic works published in 0/8. But it does not record this constant, only a list of natural logarithms calculated from it, which is usually William? Made in William Oughtred. Is it the first time that Jacob regards e as a constant? Jacob Bernoulli.
The earliest known uses of the constant e are 1690 and 169 1 year, which is represented by B. In 1727, Euler began to use e to represent this constant. E was first used in publications, and it was Euler Mechanics in 1736. Although some researchers later used the letter C, E was widely used and finally became the standard.
The reason why E is used is really unknown, but it may be because E is the first letter of the word "index". Another view is that A, B, C and D have other common usages, and E is the first available letter. However, it is unlikely that Euler chose this letter because it is the initials of his own name, because he is a very modest person and always properly affirms the work of others.
Many growth or decay processes can be simulated by exponential function. The important thing about exponential function is that it is the only function whose derivative is equal to (multiplied by a constant). E is irrational number and transcendental number (see Lindemann-Weierstrass theorem). This is the first one that is proved to be a transcendental number, but it is not intentionally constructed (compare Liouville number); Charles wrote it. Charles Hermite proved in 1873.
When x tends to positive infinity or negative infinity, the limit of the function expression (1+ 1/x) X is equal to e, which is expressed by the formula:
Lim (1+ 1/x) x = e (x tends to ∞)
In fact, E was discovered by Euler through this limit. It is an infinite acyclic decimal with a value equal to 2.7 1828. The logarithm based on e is called natural logarithm and is represented by the symbol "ln".
Logarithm (natural logarithm) and exponent based on e reveal many objective laws of nature from a mathematical point of view. For example, the differential and integral of the exponential function "the x power of e" to x is itself a function. Later generations call this law "natural law", in which E is the essence of natural law. Therefore, the above formula for finding limit e was published by the British scientific magazine Physical World on June 5438+00, 2004 as one of the "greatest formulas" selected by scientific readers, ranking second.
Leonhard euler was born in Basel, Switzerland on 1707- 1783. When 13 years old, he went to university of basel to study and got the most famous mathematician John? Johann bernoulli's careful guidance (1667- 1748).
Euler's profound knowledge, endless creative energy and unprecedented rich works are amazing! He began to publish papers at the age of 19, until he was 76 years old, and wrote a sea of books and papers for more than half a century. Today, Euler's name can be seen in almost every field of mathematics, from Euler line of elementary geometry, euler theorem of polyhedron, Euler transformation formula of solid analytic geometry, Euler solution of quartic equation to Euler function in number theory, Euler equation of differential equation, Euler constant of series theory, Euler equation of variational method, Euler formula of complex variable function and so on. His contribution to mathematical analysis is even more original. Introduction to infinitesimal analysis is his epoch-making masterpiece. At that time, mathematicians called him "the embodiment of analysis".
Euler is the most prolific outstanding mathematician in the history of science and is known as Shakespeare in mathematics. According to statistics, * * * has written 886 books and papers in his tireless life, of which 40% is analysis, algebra and number theory, 18% is geometry, 28% is physics and mechanics, 1 1% is astronomy, and 3% is ballistics, navigation and navigation. Petersburg Academy of Sciences has been busy sorting out his works for 47 years! In the history of mathematics,18th century is called "Euler era".
Euler also created many mathematical symbols, such as functions f(x)( 1734), π( 1736), log and e( 1748), sin and cos( 1748), TG (/kloc-0).
It is no accident that Euler's works are surprisingly numerous. He can work in any harsh environment. He often kneels on the ground with his child in his arms and finishes writing papers, regardless of 13 children's noise. His indomitable perseverance and tireless academic spirit made him dictate several books and about 400 papers during the 17 years after he lost his sight at the age of 59.
/kloc-Gauss (1777- 1855), a great mathematician in the 9th century, once said: "Studying Euler's works is always the best way to understand mathematics." Euler's father Paul? Paul Euler is also a mathematician. He wants little Euler to study theology and teach him a little at the same time. Because of little Euler's talent and unusual diligence, he was also influenced by John? Bernoulli's appreciation and special guidance, when he wrote a paper about masts at the age of 19, and won the prize of the Paris Academy of Sciences, his father no longer opposed him to study mathematics.
1725 John? Daniel bernoulli's son? Bernoulli went to Russia and recommended Euler to Tsar Cadling I, so Euler came to Petersburg on May 1727. 1733, at the age of 26, Euler became a professor of mathematics at the Academy of Sciences in Petersburg.
1735, Euler solved an astronomical problem (calculating the orbit of a comet), which took several famous mathematicians several months to solve, but Euler used his own invented method and completed it in three days. However, overwork made him suffer from eye diseases and unfortunately lost his right eye. At this time, he was only 28 years old.
174 1 year, at the invitation of Peter the Great of Prussia, Euler went to Berlin as the director of the Institute of Physics and Mathematics of the Chinese Academy of Sciences until 1766, and later returned to Petersburg at the sincere invitation of Tsar Cadling II. Unexpectedly, not long after, his left eye vision dropped sharply and he was completely blind.
Unfortunate things followed. 177 1 year, the Petersburg fire damaged Euler's residence. Euler, 64, was sick and blind and trapped in the fire. Although he was saved from the fire by others, his research and a lot of research results were reduced to ashes.
The heavy blow still didn't make Euler fall, and he vowed to get the loss back. After Euler was completely blind, he still fought against the darkness with amazing perseverance and studied with memory and mental arithmetic until his death, which lasted 17 years. Euler's memory and mental arithmetic are rare. He can retell the contents of his notes when he was young. Mental arithmetic is not limited to simple operations, and advanced mathematics can also be done by heart. During the blind 17 years, Euler also solved Newton's headache about the moon deviation and many complicated analytical problems.
Euler has a high style. Lagrange is a great mathematician after Euler. Since the age of 19, he has been communicating with Euler to discuss the general solution of isoperimetric problems, from which the variational method was born. The isoperimetric problem has been carefully considered by Euler for many years. Lagrange's solution won warm praise from Euler. 1June 2, 759, Euler praised Lagrange's achievements in his reply, and all mathematicians in Europe respected him as a teacher in his later years. The famous mathematician Laplace once said, "Euler is our mentor."
Euler's energy was maintained until the last moment. 1783 One afternoon in September, Euler invited his friends to dinner to celebrate his successful calculation of the law of balloon rising. At that time, Uranus had just been discovered, and Euler wrote the essentials of Uranus orbit calculation. He also laughs with his grandson. After drinking tea, he suddenly fell ill, and his pipe fell out of his hand, muttering, "I'm dead."
Euler's life is a life of struggle for the development of mathematics. His outstanding wisdom, tenacious perseverance, tireless spirit of struggle and noble scientific ethics are always worth learning.
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, we often see important constants, formulas and theorems named after him in many branches of mathematics.
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 took the first letter e of his name as the base of natural logarithm.
In fact, Euler chose e for two reasons, which are also accepted by most people: one is that after the four commonly used letters A, B, C and D, the first letter that is not often used is e, so he naturally chose this symbol, which represents the base of natural logarithm; Another way of saying it is that e is the first letter of the word "index" in English. Although you may suspect that the Swiss Euler is not a native English speaker, it is actually the "index" of French and German. What is the origin of e? It is still a mystery.