Everyone must have learned pi when they were students, and circle-related calculations are common in some topics. The small circle can be said to hide a lot of mysteries, and the back of pi is full of many stories.
June 8
Google Cloud released a message: Computer scientist Emma Haruka Iwao, through Google Cloud's computing engine, calculated pi to 100 trillion decimal places, and broke the record of 62.8 trillion after the decimal point set by the Swiss research team in 2021.
In 1761, the German mathematician Lambert proved that pi is an irrational number, that is, an infinite non-cyclic decimal number. So now that you know it's all, what's the point of using a supercomputer to do the calculations?
If one day Pi is exhausted, what kind of impact will it have on mathematics and even the entire material world?
Circle is closely related to our lives
The calculation of Pi began to explore methods thousands of years ago by the ancients, and initially they estimated that the approximate value of Pi should be 3, but with the further development of technology, higher requirements were also put forward for the accuracy of Pi.
In the 2nd century BC, the ancient Greek mathematician Archimedes through the iterative algorithm and the concept of numerical approximation on both sides, found the lower and upper bounds of Pi 223/71 and 22/7 respectively, and finally took their average value of 3.141851 as an approximation, it can be said that Archimedes created a precedent in human history to calculate Pi through theory.
In 263 AD, the Chinese mathematician Liu Hui first used the limit-finding circumcision to calculate pi, and obtained a value of 3.14, but he found that it was still small, and finally cut the circle to 1536 sides, and found the area of the 3072 edge, accurate to 3.1416 to be satisfied.
During the Southern and Northern Dynasties in 480 AD, the mathematician Zu Chongzhi further optimized the circumcision technique, calculating that the pi was between 3.1415926 and 3.1415927, and the accuracy of seven decimal places made Zu Chongzhi lead the world for the next 800 years
Although the idea of circumcision is very clever, but the amount of calculation is very large, the more accurate the value means the greater the calculation, in the absence of a calculator, such calculation is also quite difficult, until the sixteenth century some mathematicians found that pi can be expressed in the sum or product of the infinite series of numbers, pi calculation suddenly became concise and clear.
With the blessing of the infinite number level, as long as the number of terms calculated, the more accurate the value of Pi can be obtained, but the infinite number level is inexhaustible as its name, which leads to another problem:
Is there an end to the value of Pi?
In 1761, the German mathematician Lambert used functions and special function fractions to prove that Pi is an infinitely non-cyclic decimal number, that is, irrational numbers, in addition to the characteristics of irrational numbers, the German mathematician Linmann also proved that Pi is a transcendent number, that is, the square of Pi is also an irrational number, so Pi can not be used as the solid root of the multi-root of the rational coefficient.
Since you know that Pi is inexhaustible, why do you have to calculate it?
In the common field of science and technology, only a few dozen digits after the decimal point of pi are used at most, and if you want to calculate the current observable area rate of the universe, as long as you use 40 digits after the decimal point, you can reduce the error to the size of a hydrogen atom.
So the calculation to hundreds of thousands or even millions of decimal places, from the point of view of practicality, there is no point, the reason for continuing to calculate, on the one hand, is because human beings are always willing to challenge, try to create some new records, and constantly break through the limits of self-transcendence, just like human beings, although cars have now been popularized, but the relevant track and field competitions still exist.
On the other hand, the huge amount of computation can also test the performance of supercomputers. For example, google cloud computing to the 100 billion bits took 157 days, 23 hours and 31 minutes, and 2019 31.4 trillion bits took 121 days, enough to see the progress of computing power.
If one day Pi is calculated, after troubleshooting computer failures and other external factors, it can only be said that there is a big problem with the human mathematical system, and the theory has never existed alone, so once Pi is found to be not an irrational number, it will affect the whole body.
First, if pi has an end, it proves that it is a rational number
But today's mathematical theories are based on the fact that Pi is a rational number, calculus will first encounter a crisis, and then the mathematical edifice will be clouded, and many physical formulas also have Pi, such as Einstein's gravitational equation, which describes the relationship between time and space.
If pi is wrong, it means that the universe we exist may not be what we think it is, Euclidean geometry will no longer apply, and Pi will appear as a variable.
But in the current situation, Pi should not be calculated, it is the basic law of our universe, in fact, Pi is not so magical, in different geometric directions, Pi is not irrational numbers depends on the specific situation, such as in non-Euclidean geometry roche geometry and Risgrine geometry, Pi is not a fixed value.
In fact, pi is not only used in basic theory, but also in some confidential work. For example, on social platforms and commonly used websites, the passwords we set will still have certain logic and rules, which are related to ourselves.
For some extremely confidential information and materials, it is necessary to ensure that the password is completely irregular, and Pi is a naturally irregular infinite number, so it is often used as a very secure password.