1, Euler formula: This formula relates complex exponent with trigonometric function, and shows the profound relationship among natural number, complex number and trigonometric function in mathematics. The formula is e (IX) = cos (x)+I * sin (x).
2. Fourier series: Fourier series is a method to decompose any periodic function into a series of sine and cosine functions, which shows the relationship between periodic function and trigonometric function. The formula is: f (x) = a _ 0/2+σ [a _ n * cos (NX)+b _ n * sin (NX)].
3. Euler-Fermat Theorem: This theorem shows that there is no integer solution equation x n+y n = z n for any integer n greater than 2, and the proof of this theorem reveals the law of prime number distribution in mathematics.
4. Pythagorean Theorem: This theorem describes the relationship between the length of hypotenuse and the length of two right-angled sides of a right triangle. The formula is c 2 = a 2+b 2.
5. Golden ratio: The golden ratio is an irrational number, and its value is about 1.6 180339887. The golden section has many beautiful properties in mathematics and nature, such as Fibonacci sequence and pentagram shape.
Application of mathematical formula
Mathematical formula is an abstract way to describe mathematical relations and laws. They are put forward in a concise form and provide a powerful tool for solving practical problems. Mathematical formulas are widely used in science, engineering, economy and computer fields. As an advanced way of thinking, Fourier transform is widely used in physics, electronics, number theory, combinatorial mathematics, signal processing, probability theory, statistics, cryptography, acoustics, optics, oceanography, structural dynamics and other fields.
Mathematical formulas play an important role in physics.
18th century is the golden age of combining mathematics with classical mechanics. /kloc-in the 0/9th century, mathematics was mainly applied to electromagnetism, and the School of Mathematical Physics of Cambridge University came into being. The most representative achievement is Maxwell's electromagnetic equation, which consists of four concise partial differential equations.