Do you know that it’s Pi Day today?

What is the value of pi? Although it was not until the 18th century that the German mathematician Lambert first proved that pi is an irrational number, that is, an infinite non-repeating decimal, mathematicians in ancient times had already discovered that the ratio of a circle’s circumference to its diameter could not be expressed as an exact numerical value. Calculating a more precise value for pi has been a continuous endeavor of mathematicians generation after generation. The ancient Greek mathematician Archimedes was a pioneer. By using iterative calculations of the circumscribed and inscribed regular polygons of a circle, he estimated that the value of π lies between 223/71 and 22/7. In this regard, ancient Chinese mathematicians made significant contributions. During the Eastern Han Dynasty, Zhang Heng, the inventor of the seismograph, used the ratio of the area of a square to that of its inscribed circle to refine the value of pi to approximately 3.16. Liu Hui, who lived not too far apart in time from him, took a different approach: by constructing regular polygons inscribed within circles, he was able to determine a relatively more accurate value for pi. His method came to be known later as the method of cutting circles. The more finely it is cut, the less is lost; keep cutting until it can no longer be cut any further, and then it becomes one with a circle, with nothing lost. ——Liu Hui started with a regular hexagon inscribed in a circle and calculated up to a regular 3072-sided polygon inscribed in the same circle, arriving at the value π≈3.1416, thus taking another step forward in his calculations. Later on, there was the famous Zu Chongzhi, who was the first in the world to determine the value of pi with precision between 3.1415926 and 3.1415927. It is no longer possible to determine whether he obtained this value by further dividing a circle based on Liu Hui’s work. The only thing we can be certain of is that to calculate pi to this precision, it is necessary to use a 24,576-sided polygon inscribed in a circle. In an era when Arabic numerals did not yet exist, it must have been extremely difficult to arrive at this number using only simple abacuses.

The first person to use the Greek letter π to represent pi was the 18th-century British mathematician William Jones. Pi is the 16th letter of the Greek alphabet, and it is also the first letter of the Greek word for \"perimeter\". In 1737, the great Swiss mathematician Euler also began using π to represent the value of pi, and since then this notation has become widespread. Because it sounds like the English word “pie,” π is also used as a joke by tech enthusiasts. On March 14, 1988, Larry Shaw, a physicist at the San Francisco Exploratorium in the United States, led museum staff and participants on a circular journey around the museum’s monument for 3 and 1/7 laps (22/7, one of the approximations of π), during which they ate fruit pies and shared knowledge about π. Later, the San Francisco Science Museum carried on this tradition by holding celebrations on this day each year, which is the origin of Pi Day. The Massachusetts Institute of Technology in the United States was the first to propose designating March 14th (which represents 3.14) as **National Pi Day**. In 2009, the U.S. House of Representatives officially passed a resolution designating March 14th of each year as Pi Day.

I really didn’t know the date; hearing it mentioned made me suddenly realize it.

An American guy composed a piece of music based on the sequence 314159265358979323846, and the melody turns out to be quite pleasant to listen to.

3.14, 15:09:26; P

Is it useful to calculate up to 20 trillion decimal places?