Have you ever wondered what would happen if π was exhausted?

Origin of pi

π is pi. It took human beings 4000 years to prove that it is an irrational number, and it was ranked as the last irrational number, which is one of the representatives of irrational numbers. Because this number is so common in life, it is so common that people almost forget its importance.

When we were in elementary school, we learned about pi, and we still use this π until we learn about Fourier transform . Obviously, one has to do the calculation with a number a little bit smaller than three.

To give the simplest example, everyone has seen the reversing radar. Why can the reversing radar rely on the vibration of sound waves to track obstacles? This requires the use of FFT, which is Fast Fourier Transform . It combines high-speed hardware to realize real-time tracking and processing of signals.

It can be said that FFT has laid the foundation for the development of modern digital signal processing equipment . And this Fourier transform needs to use this π in the operation. So, how did this π come about?

As early as the 20th century BC to the 17th century, traces of pi calculations can be seen on a stone plaque in ancient Babylon. It's just that people just roughly divided 25 by 8 and got the number 3.125 .

At this time, the pi calculated by people was not accurate, but they already knew that it was a number slightly larger than 3 . Until Archimedes in ancient Greece corrected pi to 3.14.

Later, Liu Hui in the Wei and Jin Dynasties calculated pi to 3.14159, and Zu Chongzhi in the Southern and Northern Dynasties calculated it to seven decimal places. This value was already very accurate at that time.

Until the 15th century , the Arabic mathematician Qasi accurate π to 17 decimal places. In the 17th century , someone calculated π to 35 decimal places and so on.

So far, people have been able to calculate π to 100 trillion decimal places with the help of supercomputers , but this is far from enough.

math crisis

The first mathematical crisis was the discovery of the root sign 2 , which showed that some truths of geometry have nothing to do with traditional arithmetic, and that sets cannot be represented by integers.

This discovery directly impacted the Pythagoras School , which dominated the Western mathematics field, and led European mathematicians to regard geometry as the basis of all mathematics. This abnormal development is still spreading in Europe until now.

The second mathematical crisis is the widely circulated "Achilles can't catch up with the tortoise" , which is also called Zeno's paradox. Due to the appearance of calculus, the contradictions of "infinitely large" and "infinitely small" appeared. As for the consequences, needless to say. Until now, there are people on the Internet who are arguing about which is greater, 1 or 0.99 infinite loop.

The third mathematical crisis occurred in the electrical age. Since Forte revealed a paradox in set theory, a group of mathematicians and physicists were skeptical about the structure of mathematics .

Everyone should have heard this story, that is, there is a barber who claims that he only shaves everyone who does not shave himself. Then, if he doesn't shave himself usually, he should follow his own rules to shave himself, but if he does, he breaks the rules he set. This is called Russell's paradox .

Bring it into the whole number, and you will find that if some mathematical collections admit infinite sets and infinite bases, then they do not meet the definition of this mathematical collection; time meaning.

Obviously, the third mathematical crisis has the most serious impact. The mathematization of logic has led to the emergence of many paradoxes , shaking the mathematical edifice that humans have worked hard to build for thousands of years.

So, once this π is calculated by people, does it mean that many mathematical problems including Leibniz formula, Fourier transform, Basel problem and so on are wrong from the beginning.

The effect of pi

As the most important irrational number in the world, π covers almost every aspect of our life . Electronic equipment, integrated circuits, track models, aviation equipment, etc.

Once π is calculated, it means that these things are wrong from the moment they are born , and technological inventions with a little bit of SLR and pi will have an impact. Is this really the case? In fact, the matter is not that serious.

Some people say that π contains all the secrets in the world, just like your bank card number, chat software password, and any confidential data are all contained in this infinite non-repeating decimal .

But if it really reaches that point, it means that human beings can know all the secrets of the universe like in science fiction. You can manipulate time and space, travel through black holes, and explore the past and future. If it really reaches this level, who would care about a small pi?

In fact, pi cannot be calculated completely. As long as there is such a thing as "circle" in the world, pi must be inexhaustible. If it is exhausted, it proves that the object is just an infinite polygon, and the curve does not exist at all.

In common scientific fields , it is impossible for people to use tens of trillions of digits after the decimal point of pi, at most it is only accurate to tens of digits after the decimal point, and it is enough to reduce the error to the size of an atom. Zero error is used in practice absolutely impossible to exist.

Therefore, it does not have any specific meaning from a practical point of view to calculate hundreds of thousands to tens of billions of digits after the decimal point. The reason people do it is nothing more than to be challenged, to explore never-ending. Using a supercomputer to calculate pi is also to test its computing power.