Circumference is accurate to 30 trillion digits, so why is it still counted? See how much good it does
Circumference is accurate to 30 trillion digits
The circumference is accurate to 30 trillion digits, so why is it still counted? See how much good it can do
Pi is an extremely well-known number, which has attracted the interest of laymen and scholars throughout the ages. As an important constant, it was originally proposed to solve calculations about circles with an urgent need for the application. It is also true that it has been one of the goals of mathematicians for thousands of years, and generations of mathematicians have dedicated their wisdom and labor to it.
History of the study of π
The study of pi has a long history: In the 3rd century B.C., Archimedes, a famous scholar in ancient Greece, studied the circumference of the circle. The ancient mathematical work "Zhou Thighs" was written in the 1st century BC. The ancient mathematical work "The Book of Thighs" was written in the 1st century B.C. There is a record of "the diagram of a circle with a hook and a square".
In the 3rd century, Liu Hui, a mathematician in China, creatively proposed the technique of cutting the circle and came up with the value of circumference as 3927/1250 (i.e. 3.1416), which determined the decimal point of circumference to 3 digits. The accuracy of this value was leading in the world at that time.
About 200 years later, Zu Chongzhi used the circle-cutting technique to calculate the circumference between 3.1415926 and 3.1415927 night after night and year after year, and mankind determined the decimal 6 digits of circumference for the first time. For more than a thousand years ahead of the world, this exquisite result, ancient and modern Chinese and foreign people do not marvel. From Liu Hui to Zu Chongzhi, their ideas, methods, and achievements in the study of pi reflect a peak reached by ancient mathematics in China, as well as a peak of ancient science in China.
The value of π has been accurate to 300,000 decimal places
In 1579, the French mathematician Veda calculated pi correctly to the 9th decimal place. The 17th century was a watershed, due to the development of mathematical theory, there are many formulas for calculating pi, and the decimal part of pi broke through 35, 100, 707 bits one after another ...... By the 1950s, the calculation of pi was again to a new level and an era of disruption because of the advent of computers. 1949, for the first time, American scientists spent 70 hours using a computer to calculate the value of pi to the 2037th decimal place.
And by 1973, someone had calculated pi to 1 million decimal places, and the results were printed into a 200-page book, arguably the world's most boring book, breaking the 1 billion mark in 1989 and exceeding 6.4 billion bits in October 1995. 1999, Japanese University of Tokyo professor Yasumasa Kaneda sought 200 billion bits of decimal values if these numbers are printed on A4 If these numbers are printed on A4-size copy paper so that each page printed 20,000 digits, then, these papers will be stacked up to five or six hundred meters. Nowadays, the circumference of the circle has been accurate to 31.4 trillion decimal places.
Already enough, why count?
However, it is not particularly surprising that the record is now broken, no matter how many digits it is advanced to. It is not very meaningful to apply the value of pi by counting it too precisely, and a dozen or so digits are sufficient for the value of pi used in modern science and technology. To quote an American astronomer to illustrate the practical value of such calculations - "Ten decimal places would be enough to make the circumference of the earth accurate to within an inch, and thirty decimal places would make the entire perimeter of the visible universe accurate to an amount that even the most powerful microscope could not distinguish ". So why do mathematicians still fight their way upward, like mountain climbers, and keep seeking instead of stopping their exploration of π? Why does its small value have such a great charm? It is probably due to the curiosity of human beings and the mentality of being ahead of others, but there are many other reasons.
The benefits of pi
First, the degree of accuracy in calculating the value of pi is one of the indicators of the level of mathematical discovery in a country. Secondly, pi can now be used by people to test or check the performance of supercomputers, especially the speed of computing and the stability of the computational process. When Intel introduced the Pentium, it was found to have a slight problem, and this problem was found by running the calculation of pi. This is one of the reasons why ultra-high precision π calculations are still important to this day.
Once again, the methods and ideas of computation can lead to new concepts and ideas. Although computers can calculate faster than anyone can imagine, after all, it still needs to be programmed by mathematicians to guide the computer to do the calculation correctly.
Finally, a benefit that is relevant to us ordinary people. Reciting and memorizing pi from time to time is a great way to exercise the brain. In the process, our brain operates frequently and improves its sensitivity to numbers, thus it is also helpful to memorize other numbers in life. It is worth mentioning that the great scientist Albert Einstein was one of the avid fans of pi.
Conclusion.
The circumference is not only related to the calculation of circles and spheres but also related to probability, statistics, physics, architecture, astronomy, and demography, it is everywhere in life.
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