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- What is π (Pi)？
In elementary school, we used to believe that π was 22/7 or 3.14, but in reality, these are just approximations of π. π is an irrational number that cannot be expressed as a fraction or a finite decimal. Long ago, people discovered that the ratio of the circumference of a circle to its diameter is a constant value, regardless of the size of the circle. This constant value is denoted by π. The mathematician Euler began using the symbol π (which represents the first sound of the word "perimeter") in 1737 to represent this fixed value. In Chinese, it is referred to as "圓周率" (yuan zhou lv).
Liu Hui's "Method of Exhaustion" is indeed a great example: "By taking smaller and smaller steps, the losses become smaller and smaller. By repeatedly taking steps, we eventually reach a point where we cannot take any more steps, and then we merge with the circumference of the circle without any loss." Liu Hui considered the inscribed regular polygons within a circle, starting from a hexagon and doubling the number of sides each time, until reaching a regular polygon with 3072 sides. The more sides there are, the closer they get to the circle. By using the relationship between perimeter, area, and diameter, Liu Hui calculated that π is approximately 3.1416.
Zu Chongzhi, building upon Liu Hui's research, further developed the method and calculated π accurately to seven decimal places by inscribing a regular polygon with 24576 sides. He also discovered the approximations of π as 22/7 and the more accurate approximation as 355/113. This discovery predates the European approximation by a whole millennium!
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In the absence of calculators and Arabic numerals, ancient scholars devoted themselves wholeheartedly to the pursuit of scientific truth, relying solely on manual calculations. Their passion and perseverance are truly admirable and worthy of our learning and admiration!
The dedication shown by these individuals in their pursuit of knowledge serves as an inspiration for us. Their unwavering commitment and determination remind us of the importance of perseverance, even in the face of challenges. Their achievements stand as a testament to the power of human intellect and the capacity for discovery and innovation.
We can learn from their example by cultivating a similar passion for knowledge and a willingness to push the boundaries of our understanding. Their legacy serves as a reminder that with dedication, curiosity, and a thirst for knowledge, we can make remarkable advancements and contribute to the progress of science and humanity.
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With the help of computers, π has been calculated accurately to over 109 decimal places. You might wonder why such precision is necessary when 3.14 seems sufficient. It's akin to asking why someone would go through the arduous task of summiting Mount Everest when they could simply climb a smaller mountain. Furthermore, people have also used the value of π to test the performance of computers.
If you are interested in using a computer to calculate π, you can visit the following website:
Asking a Mandarin teacher for help instead of a math teacher!!
３．１４１５９ ２６５３５ ８９７９３２３ ８４６.....
山巔一寺一壺酒 二侶舞扇舞 把酒砌酒扇又搧 飽死囉.....
1. In February 1995, Hiroyuki Goto recited the value of pi with 42,000 decimal places, setting a world record. He accomplished this feat in just over nine hours of memorization.
2. Albert Einstein's birthday is on March 14th, coincidentally known as Pi Day.