Pi is also expressed by the symbol π, which is specifically defined as the ratio of the circumference to the diameter of a circle.
The approximate range of pi is 3. 14 15 ... which is considered as an infinite acyclic decimal at present. You know, pi is very common in our daily life, so several ancient civilizations actually have records about pi, such as:
More than 4,000 years ago, ancient Babylon got a pi of 3. 125, and ancient Egypt got a similar value. In ancient China, Zu Chongzhi and others obtained the range of pi by secant circle: 3.1415926 ~ 3.145438+05927.
In addition to ancient Babylon, Egypt and China, some ancient countries such as India have similar records.
Secant circle method
Archimedes, an ancient Greek scholar, was the first to calculate pi rigorously by secant method, and the time was about 250 BC.
His method is to get pi by geometric algorithm of multiple regular polygons. Archimedes first calculated the side lengths of the circumscribed regular hexagon and the inscribed regular hexagon of a circle, and obtained the interval range of π.
Approaching, he changed the hexagon into a dodecagon, continued to calculate the side length, and continued to get the range of pi. Finally, the last deformation is positive 96, and the approximate value of pi is 3. 1408.
Later scholars actually continued to solve the problem on the basis of Archimedes method and got a smaller range. Around 1630, mathematicians have been able to take the value of pi to 39 decimal places, which can also be said to be the final result of secant method. Later, it was not until 1699 that mathematicians broke this record by using infinite series and calculated it to 7 1 digit after the decimal point.
Is pi really an infinite acyclic decimal?
Although we can always approach the final result of pi by secant method, mathematicians have long realized that pi should actually be an infinite acyclic decimal, which is what we often call an irrational number. Of course, if this is the case, it is even more impossible for us to prove it by calculating pi by computer.
So in this matter, a reliable mathematical proof is far more useful than continuous calculation. At 1947, there really is a mathematician named Ivan Niven.
With the help of calculus and reduction to absurdity, he proved that pi is really an irrational number through very strict logical reasoning. So pi is an irrational number, which has been proved by strict mathematics and is widely accepted.
Why do scientists calculate the digits of pi?
Since pi has been proved to be irrational by mathematics, in fact, no amount of calculation is as reliable as this mathematical proof, but scientists are very obsessed with calculating the number of digits of pi, and now it has been calculated to hundreds of millions of decimal places. For example, 20 1 1, IBM announced that their blue gene supercomputer has been calculated to 60 trillion decimal places. So what is the purpose of doing this? Is it trying to calculate pi?
In fact, the supercomputer doesn't calculate the digits of pi because it wants to calculate pi completely. After all, it has proved to be inexhaustible. At present, it is actually very simple to do this, that is, to test the computing power and stability of the CPU (Central Processing Unit) of the supercomputer. Because the calculation of pi is very complicated. Therefore, compared with ordinary computers, the calculation of pi is very difficult and prone to bugs. Similar problems have occurred in Intel's CPU before. So the purpose of calculating pi is to detect the performance of CPU and possible bugs. So pi is not the object to be tested, but a universal testing tool.
What happens if you calculate pi?
If one day, pi is calculated, of course, there is a great probability that this will not happen. This means that it has been proved wrong. As mentioned earlier, calculus and reduction to absurdity are used. So, this shows that calculus may be wrong. Specifically, we also mentioned the secant circle method above, which is to regard the circle as a regular polygon. If pi can be calculated, it means that the circle does not exist, and the seemingly smooth curve of the circle is actually composed of countless line segments, which means that the curve does not exist.
So geometry will collapse, and the part of calculus describing the curve will be considered wrong, so calculus is wrong. That means that for thousands of years, the foundation of the mathematical building developed by human beings is problematic and needs to be demolished and rebuilt. Therefore, if pi can be completely calculated, it means that human mathematics and science have returned to thousands of years ago overnight and started from scratch.