1, Introduction to Euler
Leonhard euler (Leonhard? Euler,1April 70715-1September 783 18), a Swiss mathematician and physicist, is one of the pioneers of modern mathematics. Euler/kloc-was born in Basel, Switzerland in 0/707, entered university of basel at 0/3, graduated from university at 0/5, and obtained a master's degree at 0/6.
On average, he writes more than 800 pages of papers every year, and also writes a lot of teaching materials such as mechanics, analysis and geometry. Introduction to Differential Analysis, Principles of Differential Calculus and Principles of Integral Calculus have all become classic works in the field of mathematics.
Euler studied mathematics so extensively that important constants, formulas and theorems named after him can often be seen in many branches of mathematics. 1September 783 18 died in Petersburg, Russia.
2. Introduction of Euler Formula
A r/(a-b) (a-c)+b r/(b-c) (b-a)+c r/(c-a) (c-b), when r=0. 1, the value of the formula is 0, and when r=2, it is 6544.
E ix = cosx+isinx, e is the base of natural logarithm, and I is the imaginary unit. It extends the definition domain of trigonometric function to complex number, and establishes the relationship between trigonometric function and exponential function, which occupies a very important position in the theory of complex variable function.
The identity e i π+ 1 = 0 is also called Euler formula, which is the most fascinating formula in mathematics. It connects several most important numbers in mathematics: two transcendental numbers: the base e, π of natural logarithm, and two units: imaginary number unit I and natural number unit 1 and 0, which is regarded as one of the great discoveries of mankind. Mathematicians evaluate it as "a formula created by God."
3. Philosophical discussion of Euler formula.
Gauss said: "If you can't see at a glance that Euler's formula is clearly established, this person will never become a first-class mathematician." People who are truly proficient in mathematics are almost always good at seeing through the essence of everything, and this perspective is not just the perspective of mathematics.
Significance and application of Euler formula:
1, the meaning of Euler formula
The significance of Euler's formula is that we can measure the relationship between friction and the number of turns the rope winds around the pile. On any regular spherical graph, if R is used to record the number of regions, V is used to record the number of vertices and E is used to record the number of boundaries, then R+V-E=2, which is euler theorem. Descartes first proved this theorem in 1640.
Later, Euler independently proved it in 1752, calling it euler theorem, and some people abroad called it Descartes theorem.
2. Application of Euler Formula
Euler's formula is easy to understand and has two functions. One is for polyhedron, and the other is for series expansion. Euler formula mathematics plays a vital role in it, including two transcendental numbers, the base e of natural logarithm and pi, imaginary unit and natural number unit 1, which is the greatest discovery in the history of human mathematics.
So in the eyes of mathematicians, Euler's formula should be God's formula.
The first person to prove Euler's formula was Cauchy, who was 20 years old. He affirmed the significance of Euler's formula by the method of polyhedral hypothesis. A transformation of Euler formula, Euler identity. Known as the most beautiful formula in mathematics.