The world's great mathematical versatile ---- l Analytic Number Theory Analysis of the founder of the embodiment of r Leonhard?
Leonhard Euler? Euler (L. Euler ,1707.4.15-1783 .9.18 ) is a Swiss mathematician. born in Basel, Switzerland (Basel), died in St. Petersburg (Petepbypt). father, Paul? Euler was a priest, like math, so Euler's childhood influenced by this. But his father bent so that he studied theology in order to pick him in future classes. Fortunately, Euler did not take his father arranged for him the way. father went to school in the University of Basel, and was a famous mathematician John? Bernoulli ( Johann Bernoulli ,1667.8.6-1748 .1.1) and Jacob? Bernoulli (Jacob Bernoulli ,1654.12.27-1705 .8.16) sort of friendship. Because of this relationship, Euler made the acquaintance of John's two sons : good at math Nicholas (Nicolaus Bernoulli ,1695-1726) and Daniel (Daniel Bernoulli ,1700.2.9-1782 .3.17) and his brother, (both of whom later became a mathematician.) They are often to small European Pull the story about a lively and interesting mathematical mathematical knowledge. These are the Euler benefit .1720, by the John Paul lift, only 13-year-old University of Basel, Euler became a student, and John carefully nurtured a bright Euler. When John found that the knowledge of the classroom can not meet the desire for knowledge of Euler, it decided to give him every Saturday afternoon alone counseling, answers and teaching. John's efforts were not wasted, in his rigorous training, the European Pull finally grow up. he was 17 years old, became the first ever Basel, a young master, and became John's assistant. under the guidance of John, Euler chose from the start by addressing the practical problems of mathematical research Road .1726, the 19-year-old Euler as the author of This history is inseparable with him. Of course, Euler's talent there is another important factor, is his amazing memory!, he can recite a hundred before the first ten prime power, can recite Rome Virgil (Virgil) epic Aeneil, able to recite all of the mathematical formula. until his later years, he can repeat the entire contents of the notes was young. advanced math calculations done he carefully considered.
Despite his talent high, but without John's education, the result is hard to imagine. As John? Bernoulli with its rich experience and profound development of mathematical understanding of important pointers to give the Euler, the Euler began to learn that, though difficult to learn but it is very necessary book, less take a lot of detours. this history a great impact on the Euler, Euler became a great scientist that still do not forget that after the new education, which is mainly reflected in the preparation of textbooks and direct culture of the mathematics talented workers, including later became a great mathematician Lagrange (JLLagrange ,1736.1.25-1813 .4.10).
Euler Although it is not my teacher, but he Teaching more than anyone else. He being the world's foremost scholars, professors, shouldering the burden of solving advanced topics, but it can ignore the Introduction to infinitesimal analysis Euler who copied the book. Euler and other mathematicians in this area, such as Gaussian (CFGauss ,1777.4.30-1855 .2.23), Newton (I. Newton ,1643.1.4-1727 .3.31) are all different, First, the books they have written a small number, the second is incomprehensible and difficult to understand, others find it difficult to read. And Euler not only easy to understand the text, called a model in this regard. He never compressed words, always relish the his great interest in ideas and write a wide range of sound and color. He used German, Russian, English and published a large number of popular articles, but also prepared numerous primary and secondary school textbooks. He wrote the textbook of elementary algebra and arithmetic to consider carefully, describing a section right. He described many new methods of thought, making these books both tight and easy to understand. Euler number of the first to define the power of the inverse operation, and first discovered the value of the number is infinite. He proved that any non-zero real number R has infinitely many pairs. Euler to trigonometry as a system of scientific, first given by the ratio of the definition of trigonometric functions, which previously has been in his long line as defined. Euler's definition of the Research Triangle trigonometry table just out of this circle. Euler made the whole analytical trigonometry study. In the past, each formula launched only from the figure, most of the narrative expression. never the first few Euler formula derived analytically all triangle formulas, also received a number of new formulas. Euler with a, b, c, said the three sides of a triangle, with A, B, C that the first two edges right angle, so that the narrative greatly simplified. Euler's famous formula by:
again link up trigonometric and exponential functions.
in education and scientific research, Euler realized that the simplification and symbols rules of both contribute to student learning, and help the development of mathematics, so the Euler created many new symbols. as with sin, cos and so that trigonometric functions, with e denotes the natural logarithm, with f (x) that function with s that sum, with the imaginary number i said so. Euler pi p, although not first, but it is only possible through the initiative of Euler widespread. Moreover, Euler also e, p, i united in a relationship where stunning. Eulerian time series in the study cited Ru Oula constant C, which is the second p, e after another important number.
Euler not only the importance of education and talent . then only 19 years old Lagrange, France, and Euler has 48 years of age. Lagrange and Euler communications discuss results of Euler to pressure their papers, so that the Lagrangian first issued, made him famous.
Euler 19-year-old graduated from college in Switzerland did not find a suitable job in the spring of .1727, he was in Basel Department of trying to serve as director of the vacant positions, but without success. this time, St. Petersburg, Russia, ASTRI has just been established, scientists are being recruited across the country, extensive collecting talent. has been employed in the work of Daner Petersburg? Bernoulli know Euler's ability, so he tried to employ Euler to Russia. In this case, Euler left their homeland. As Daniel's recommendation, in 1727, Euler was invited to St. Petersburg to do Daniel's assistant. in the St. Petersburg Academy of Sciences He successfully won the post of associate professor of higher mathematics .1731, then was appointed leader of Theoretical Physics and Department of Experimental Physics, the work of .1733, the only 26-year-old back to Switzerland, to succeed Daniel Euler became professor of mathematics and St. Petersburg Department of Mathematics, Academy of the leaders.
During this period, Euler hard work, and published a large number of excellent mathematical papers, and other aspects of the papers, writing.
is based on classical Newtonian mechanics laid, and Europe pull is the main architect .1736, the Euler published the speed and acceleration problems in the speed and the application of the concept of vector.
same time, he founded the analytical mechanics, rigid body mechanics, research and development of the elasticity theory, the vibration theory and mechanics of materials. and he applied to the vibration theory of music The theory went, in 1739, published a book of music theory .1738, the French Academy of Sciences established the thermal nature of the problem answer the essay prize, Euler's as the molecular nature of the thermal vibration.
Euler's most distinctive features of the problem is: the mathematics of his hand deep into the deep nature and society. He was not only an outstanding mathematician, but also the location theory with practice and master, master of applied mathematics. He likes to engage in certain specific problems, not as modern as some mathematicians, the general theory of thermal failure in practice.
Euler studied because of the problems are and then actual production, and other social needs and military needs are closely linked, so Euler's creative talents into full play before, has made remarkable achievements. Euler engaged in scientific research, while also being applied to practical mathematics, the Russian Government to solve the many scientific problems, to make an important contribution to society. If the canal rehabilitation programs Fino, palace drainage design validation, preparation of teaching materials for schools, help the government mapping map; in the Weights and Measures Committee's work, participants studied the accuracy of various scales. In addition, he also writes reviews for the Academy of official publications and has long presided over the Committee's work. He is not only a lot of work for the Academy of Sciences, and lectured at the university out of time for public speaking, writing science articles for the weather departments to provide astronomical data to help design the structure construction unit mechanical analysis of .1735, the Euler tackle an astronomical calculation of the comet's trajectory problem (the problem subject to several well-known mathematician months of hard work to complete.) Euler used his invention of the new method, only three days time. three days of continuous exertion, but also Euler overwork, disease, the age of 28, Euler's right eye. such a disaster did not yield to Euler, he is still fascinated by science, selfless work. but because of Russia's long-ruling power struggle, increasingly affect the work of Euler, Euler was so depressed. things have happened that the King of Prussia Frederick the Great (Frederick the Great ,1740-1786 in office), after that the situation of Euler, Euler will be invited to Berlin. Although Euler is love their second home (where he lived for 14 years general work ), but to science, in 1741 he temporarily left the St. Petersburg Academy of Sciences, to the Berlin Academy of Sciences, worked, any director of the Institute of Mathematical Physics .1759 became the leader of the Berlin Academy of Sciences. work in Berlin, he has not forgotten Russia letters to guide him through his students in Russia, and sent his own scientific work in Russia, the development of Russian science played an important role.
during his work in Berlin, will be successfully applied to other scientific mathematics technology, to write hundreds of papers, many of his life during this period significant results are obtained. such as: a huge impact, In addition, he studied astronomy, and with the d'Alembert (ILRD'Alembert ,1717.11.16-1783 .10.29), the Lagrangian together to become the founder of celestial mechanics, issued a the movement of the fluid nature of the ideal set up the basic differential equations of fluid motion, issued the And also a subject to apply the results obtained by other disciplines. For example, he created his own ideal of the basic equations for fluid flow of blood to the biology of his contribution to add on, he hydrodynamics, tidal theory, enrich and develop the design and manufacture of ships and sailing theory, published a so, he also solved a large number of Prussia Kingdom of the actual social problems .1760 until 1762, the Euler should be invited to Charlotte, Princess of Wales's correspondence philosophy, physics, cosmology, theology, of science, music, etc., these communications Euler fully reflects the profound knowledge, cultivation of high literature, philosophy, self-cultivation. was to compile these communications
since 1741 Euler left St. Petersburg after the Russian political situation has been bad, the regime change several times, finally falling into the hands of leaf Kajielinna II, she learned the lessons of the past, began working Wenzhiwugong. her side with Voltaire, Diderot and other French Enlightenment scholars communications, he has also recruited four scientists to the Petersburg Academy of influential positions. Euler naturally became the object of her principal hired .1766, the year has been his sixtieth of the Euler invited back to St. Petersburg, the Russia prepared for his excellent working conditions.
then Euler's scientific work has been a fruitful thinking has matured. except for some special needs to continue to study, he hopes in later years of the past achievements as a summary of the system, publishing several books of high quality. However, bad luck once again to hit him. As the Russian climate, as well as tired of his work, Euler's left eye and blind, and from Euler into a pitch-dark darkness. But Euler is strong, he dictated, others continue writing method of recording. He started to concentrate on writing the , the Euler system, elaborated since the invention of calculus, the achievements of all the integral calculus, which is full of insights .1768 Euler, the In the same year, he dictated written as 1771, St. Petersburg, a fire, seeding, and Euler's residence, surrounded by the Euler fire. In this critical moment, a servant of the Euler risking their lives back from the fire out. Euler Although spared in the difficult, but his books and a large number of research results are reduced to ashes. all the hardships, the Euler did not ruin. After the fire he immediately into the new creation. Data were burned, he was blind In this case, he fully With strong will and amazing perseverance, memories of that ever. Euler's memory are indeed rare, he can recite the complete contents of the notes a few decades ago, of course mathematical formula able to recite such flow. Euler's reasoning process always thought very fine, and then dictated by his eldest son record. He also published a paper this method more than 400 articles and a number of monographs, which accounted for almost all of his writings More than half of .1774, he put his many years of variational problems focus on the outcome of a book published points system. In addition, Euler astronomy in the . In order to better carry out astronomical observations, he has studied the optical, telescopes and microscopes. effects of light through various media, color separation phenomenon and the effect of the principle put forward a complex objective, published a monograph on optical instruments , the design of the telescope and microscope have made seminal theoretical calculation of the contribution, in 1771 he published a summary of the book writings, even after his death, he left many manuscripts also enrich 47 years after the St. Petersburg Academy of Sciences. to research in terms of Euler in mathematics or the natural history of the leading history of science.
as such a scientific giant, in life he is not a rigid person. his gentle, cheerful, and sociable. Euler married twice, had 13 children. he loved his family life and children often together to do scientific games, tell stories.
Euler exuberant energy and spirit has been insisting to the study of life in the last minute .1783 afternoon of September 18, Euler and granddaughter while teasing play, I keep thinking about computing Uranus's orbit, suddenly, he slipped from his chair, his mouth whispered: Indeed few, and some historians Euler and Archimedes, Newton, Gauss as the greatest contribution to the history of the four mathematicians, they all have one thing in common basis, that is purely theoretical at the same time creating also apply these mathematical tools to solve a large number of astronomy, physics and practical aspects of mechanics, their work is interdisciplinary, and they continue to learn from the practice of rich nutrition, but not satisfied with the specific problems, and is the universe as an organic whole, trying to reveal its secrets and inherent laws.
the excellent work of Euler, future generations are highly respected famous mathematician Euler. great mathematician Laplace (PSM de Laplace ,1749.3.23-1827 .3.5) S & P said: Research work will still be the best in different areas of mathematics school, and no other alternative to it also the history of one of the greatest mathematicians.
1707 was born in Basel, Switzerland (Basel) city, a child he was particularly fond of mathematics, under 10 years old began learning Several teachers have not read, can be read with great interest but little Euler encountered do not know where to use a pen to make a mark, others ask again later entered the University of Basel .13-year-old study, which at the time is a miracle, he hit the mathematical community. small Euler is the university, but also the youngest Swiss university students on campus. in college was the most famous mathematicians have calculus authority of John? Bernoulli (Johann Bernoulli, 1667-1748) of the careful guidance, and gradually built up a strong friendship with. John? Bernoulli was once praised excel the predecessors that the students: Adult brought him. .
Euler's father, Paul? Euler (Paul Euler) is also a mathematician, had hoped the small Euler theological, and teach him a little math. Because only a small Euler's incredibly hard and the spirit, but also by John? Bernoulli's appreciation and special guidance, at the age of 19 when he wrote a paper on the mast, the Paris Academy of Sciences of the prize money, his father had not opposed his study of mathematics.
1725 of John? Bernoulli's son, Daniel? Bernoulli went to Russia, to the Tsar Kade Linyi Shi Euler recommended, so that in the May 17, 1727 .1733 Euler arrived in St. Petersburg, at age 26 Euler-year-old St. Petersburg Academy of Sciences as a professor of mathematics at .1735, the Euler solved a problem in astronomy (calculated cometary orbit), this problem after several months of efforts of the famous mathematician solved the Euler was invented his own method, three days is complete. But he had too much work to eye, and unfortunately a blind right eye, and when he was 28 years old should be 普鲁士彼德烈 .1741 Euler Great on the invitation to Berlin Academy of Sciences as director of physics and mathematics until 1766, later Tsar Kade Liner Shi returned to St. Petersburg under the sincere Duipin, unexpectedly did not take long, left eye vision loss, and finally total blindness. Unfortunately, things coming up, Great Fire of 1771 bring disaster to the Euler Petersburg home, sick and blind Euler, 64, was trapped in the fire, although he was someone else saved from the flames out, but his study and a lot of research into all ashes.
blow, still did not make Euler fall, he vowed to recapture the loss. before he completely blind, can see things dimly, he held on to the last moment, a big blackboard in the the book he found the formula illness, and then say its contents, by his students, especially the eldest son A? Euler (mathematician and physicist) transcripts. Euler total blindness later, still dark with amazing perseverance and struggle, with to study memory and mental arithmetic, until his death, as much as 17 years.
1783 年 9 18, in the recently completed calculation of the balloon rising just Euler law, in the excitement suddenly stopped breathing, at age 76 . Euler's life, worked three countries: Switzerland, Russia, Germany, regarded as his mathematician Euler, are proud to have him.
Euler's memory and mental arithmetic ability is rare, he Notes to repeat the content of young age, mental arithmetic is not limited to simple operations, like the higher mathematics can be carefully considered to complete. illustrates an example of his ability, Euler's two students to a complex of 17 Convergent Series add up, count to 50 digits, a unit difference between the two, in order to determine exactly who is Euler's intentions count for all operations, and finally find out the error. Euler in the 17 years of blindness; also address the Newton headache problem and many months away from the analysis of complex problems.
Euler's style is very high, the Lagrangian is later in the great mathematician Euler, and Euler from the age of 19 communication, discussion The general solution of isoperimetric problems, which lead to the birth of variations. isoperimetric problem is painstakingly over the years to consider the question of Euler, Lagrange's method, Euler won warm praise, October 2, 1759 Euler Sheng said in reply Lagrange's achievements and pressure modestly more mature in this respect their work temporarily released so that the job of young Lagrange published and circulated, and won a great reputation. his later years, when all European mathematicians regard him as a teacher, a famous mathematician Laplace (Laplace) once said: moment, September 18, 1783 afternoon, the Euler calculated the balloon rose to celebrate his successful law, please friends to dinner, then days, Wang Xinggang found soon, Euler wrote the calculated orbit of Uranus essentials, but also, and his grandson laugh, after tea, a sudden onset of disease, pipe fell from the hands, mouth and murmured: knowledge, endless energy and an unprecedented wealth of creative works are amazing endless! he began to publish papers from 19 years old until 76 years, wrote more than half a multitude of books and papers. can be said that the European Pull the most prolific in the history of science a distinguished mathematician, according to statistics his tireless life, wrote a total of 886 books and papers, including analysis, algebra, number theory 40%, 18% geometry, physics and Mechanics 28%, 11% of astronomy, ballistics, marine science, architecture and other 3%, St. Petersburg Academy of Sciences to organize his work, a full forty years busy. to this almost every field of mathematics can be Euler's name to see from elementary geometry of the Euler line, polyhedron of Euler's theorem, three-dimensional analytic geometry of the Euler transformation formula, the Euler solution of four equations to the Euler function in number theory, differential equations for the Euler Equations , the series of the Euler's constant, Euler's equation of variations, complex function of the Euler formula, etc., count them. his contribution to mathematical analysis is more distinctive, his epoch-making masterpiece, was a mathematician who called him the child in her lap to finish a paper, also regardless of the child in the next uproar. his indomitable spirit of perseverance and tireless scholarship, so he was blind then, did not stop the research in mathematics, 17 years after the blind, he also dictated several books and 400 papers about the great mathematician Gauss .19 century (Gauss ,1777-1855 years) said: br> Euler's life, the development of mathematics and the struggle for life, his outstanding wisdom, perseverance, tireless fighting spirit and lofty scientific and moral, is always worth studying. Euler in mathematics, physics, astronomy, architecture and even music, philosophy, have made brilliant achievements. in all fields of mathematics, often seen in Europe, named formulas, theorems, and important constants. textbook, such as the common p (1736 年), i ( 1777), e (1748 年), sin and cos (1748 年), tg (1753 年), x (1755 年), s (1755 年), f (x) (1734 years), which have all established and promotion. Goldbach conjecture Goldbach is in his correspondence with the initiative. Europe to also complete the movement of the moon around the earth exact theory, the creation of analytical mechanics, rigid body mechanics and other mechanical disciplines, deepening the telescope microscope design theory of computation.
to life in Europe can achieve great success because: a remarkable memory; concentrate, from the interference from noise and bustle; calm, tirelessly.
2007, the Swiss mathematician , physicist and engineer Leonhard? Euler (Leonhard Euler) anniversary of the birth of 300.
Euler is considered the most splendid achievements of human history, one mathematician. In many branches of mathematics and can see a lot of the Euler named constants, formulas and theorems, and his work makes the math much closer to the present form. He not only number of scholars to contribute more to promoting mathematics to almost the entire field of physics. In addition Euler also involved architecture, ballistics, marine science and other fields. Swiss Education and Research Charles Kleiber, Secretary of State said: Plath believes that: read Euler, he is all the history of mathematics teacher
recognized four of the greatest mathematicians are: Archimedes, Newton, Euler and Gauss. Archimedes Germany has the field can see the names of Euler Euler line mm Elementary Geometry, Euler polyhedron theorem, three-dimensional analytic geometry of the Euler transformation formula for the Euler function of number theory, calculus of variations of the Euler equations, complex function of the European Euler formula hh pull the most prolific history of mathematics or mathematicians, 886 kinds of books in his life wrote papers, wrote an annual average of more than 800 pages, St. Petersburg Academy of Sciences to organize his work, a full busy for 47 years. his book and so on, making the mathematical formulation is easier to promote. and, Euler to mathematics applied to many areas outside mathematics.
1707 年 Euler was born in Basel, Switzerland, 13 years old admitted to the University of Basel, 15-year-old university graduate, 16-year-old received a master's degree, 19-year-old began to publish papers, the age of 26 as the St. Petersburg Academy of Sciences, Professor, blind right eye about 30 years old, 60-year-old totally blind, Euler 1783 death of 76-year-old St. Petersburg in Russia. the blind later, he still completed the oral form of several books and over 400 papers, so that Newton solved the headache of the month from the complex issues.
great French mathematician Laplace read once said something mm Euler, he is everyone's teacher. Academy of Mathematics and Systems Science researcher Wen-Lin Li, said: constants, formulas, equations and theorems, and he makes the science closer to explore the shape we are now. In 1687, Newton in instability, the limited scope of application expanded group of mathematicians .18 century calculus, and produce a series of Extension of the application of new branches, the branch itself together with the formation of calculus known as the areas. Wen-Lin Li, said: , geometry, analysis of the three pillars of the situation. Without their work, the calculus can not spring garden, opened up the situation may be withered and barren. Euler in which the contribution is fundamental, is revered as the incarnation of l analysis r. not strict, and sometimes equal to zero and sometimes participate in operations known as involves a small amount of function and its Method of Calculus. And Euler greatly advanced calculus, and develop a lot of skills.
When the steam engine as the main body of textile machines and other technology is widely used, but without calculus, there is no analysis of the mechanical movement can not be accurately calculated with the changes. description of movement is still the most effective tool, the method statement in textbooks, many are Euler's contributions. More importantly, Newton, Leibniz calculus object is a curve, while the Euler clear that mathematical analysis The center should be function, for the first time emphasized the role of the function, and made to deepen the concept of function.
from the calculus of variations, and later ...
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