17 Big mathematical equations to change human history

In the author's opinion, there are two kinds of universal language in the universe, one is mathematics, the other is art. Mathematics in the most concise way, the complex phenomenon of the universe and the law of the most vividly revealed, is the so-called universe does not speak, great beauty! In 2013, the mathematician and popular science writer Ian Stewart published his book, "17 equations to change the world", explaining the 17 greatest equations in human history.

Now, let's take a look at the most beautiful language in the universe!

1. Pythagorean theorem

The Pythagorean theorem must be familiar to everyone, this is one of the most basic formula in mathematics, the description is right triangle three side length relationship. "Hook three strands of four strings five" read the catchy.

2. Logarithmic function

The logarithmic function is the inverse of the exponential function, which helps us to solve the problem of how many times it takes to get a number at the bottom of a number, by an exponential explosion.

The equation log (ab) = log (a) + log (b) is one of the most important of the logarithmic functions, it realizes the mutual transformation of "multiplication" and "addition". In the development of computer technology, this has played an important role in the improvement of computational speed in physics, astronomy and engineering.

3. Differential equations

This equation gives the concept of derivative in calculus, the derivative describes the local nature of the function, and the derivative of a point describes the rate of change of the function near the point. For example, if you want to know the speed at which an object is at a certain moment, then only the derivative of the distance equation at that point is required, and if you want to know the acceleration of an object at a certain moment, then only the derivative of the velocity equation at that point is required.

In scientific research, it is important to understand the changing state of an event, so the meaning of the equation is conceivable.

4. Law of universal gravitation

The man who was hit by an Apple accidentally discovered the great equation. This is the greatest scientific achievement of the 17th century and a monument to the history of human science. It unified the ground movement with the celestial movement, almost perfectly for more than 200 years, until a man named Einstein proposed general relativity.

5. Imaginary numbers

The categories of mathematics continue to expand, from natural numbers to negative numbers, fractions, to real numbers. The term imaginary is founded by the famous mathematician Descartes of the 17th century. The real and imaginary numbers together lead to the concept of complex numbers (A+BI). Mathematically, the complex numbers are incredibly sophisticated, and when we extend calculus to the plural, we find the amazing symmetry of mathematics and other properties. These characteristics play an important role in the processing of electrical signals.

6. Orado Surface formula

This formula describes an attribute of a polyhedron in which v represents the number of vertices of a multipatch, E represents the number of edges, and F represents the number of polygons. The most intuitive meaning of this formula is to describe a basic mathematical law, and more importantly, it introduces a new geometry----------------------a branch of mathematics that is significant to modern physics.

7. Normal distribution function

The image of the normal distribution function has an obvious characteristic--the middle high side is low, symmetrical distribution, like a mountain. In statistics, normal distribution functions are ubiquitous and widely used in physics, biology, and social sciences. One reason this function is so common is because it describes the behavior of a large number of independent processes.

8. Wave equation

The wave equation is a differential equation that describes the phenomenon of volatility introduced by Maxwell's equations. The physical meaning of the equation is enormous, and it inspires Einstein to propose special relativity.

9. Fourier transform

For understanding a more complex wave, we have to rely on the Fourier transform. The Fourier transform can decompose the chaotic equations satisfying certain conditions into a linear combination of trigonometric functions or their integrals, which greatly simplifies the function. Fourier transform is the core of modern signal processing and analysis.

10. Navid-Stokes equation

Similar to the wave equation, which is also a differential equation, describes some of the characteristics of the fluid, suitable for establishing a fluid model. The progress of computer technology makes the solution of Navid-Stokes equation get the development of real meaning.

11. Maxwell Equation Group

Maxwell's equations were one of the greatest discoveries of the 19th century, demonstrating the graceful symmetry between the electric and magnetic fields. The equations consist of a Gaussian law describing how charges generate electric fields, a Gaussian magnetic law that describes the absence of a magnetic monopole, a Maxwell-ampere law describing how the current and the time-varying electric field generates a magnetic field, and a Faraday's sense of law that describes how a time-varying magnetic field generates an electric field. 4 Equations.

Maxwell's equations belong to classical electromagnetics and are suitable for describing macroscopic phenomena, but when it comes to microscopic fields, it is necessary to take into account the effects of quantum effects, so as to introduce quantum mechanics to explain them.

12. Second Law of thermodynamics

First of all, this formula is not "" Pan see Trunk to throw Suwa rdquo, this is the great second law of thermodynamics. One of the manifestations of this is that in a closed system, entropy will only remain stable or increase, and cannot be reduced. It also introduces the theory of "heat Stillness", which describes the whole universe, and shows that the universe will eventually reach a dead state of eternity with entropy increasing.

13. Mass Energy equation

Einstein may be the messenger of God sent to Earth, his theory completely subvert the human world view, fundamentally changed the direction of physics. The mass energy equation creatively points out the relationship between mass and energy, which plays a key role in the development of atomic bombs. boom!!!

14. Schrodinger equation

Schrödinger, the dead and alive cat, we're all familiar with it. The Schrodinger equation is an important formula in quantum mechanics. General relativity explains the macroscopic phenomena in the universe, which is applied to the microcosm and can be used to describe the behavior of atoms and subatomic atoms. Modern quantum mechanics and general relativity are two of the most successful theories in history, and they have successfully predicted all the phenomena we have observed at the moment.

Quantum mechanics is essential for modern technology, such as nuclear power, semiconductor computers, and lasers, all based on quantum phenomena.

15. Information theory

The above equation is the entropy of information presented by Shannon, as in the previously mentioned thermodynamic entropy, which is also a quantity used to describe disorder. We often say that there is a lot of information, but how big is it?

Until 1948, the concept of "information entropy" was put forward to solve the problem of quantification of information, so that information can be carried out in mathematical research. Seriously, we can play so happily on the internet and thank it!

16. Chaos theory

This equation describes a dynamic system in which a certain amount of variation (xt+1) is associated with its current state (XT) over a period of time. where k is a specific constant, for K has been determined, the initial value of x is different, the development of events is greatly different. I believe that the butterfly effect is well understood, which is a manifestation of chaos theory. Maybe one day you accidentally put a fart, will cause a storm in Washington, D.C.

17. The Lake-Scholes equation

This is another differential equation that describes how financial experts and traders can price derivative financial products (such as equities, bonds, currencies, and Commodities), which provides strong guidance and assistance to financial practitioners.

After reading these, you may feel a lot of déjà vu, or see a big head. But one thing to be sure, aside from the profound connotation of mathematics, its form is so beautiful, concise and mysterious!

PS: Unexpectedly leaked the Oura equation--e^ (iπ) + 1 = 0! The Oura equation joins the 5 most basic constants in mathematics in the simplest way, with no extra part, which is definitely the most beautiful mathematical formula in history, not one!

17 Big mathematical equations to change human history