π Day

Do you know today, March 14, is Pi Day? And 1:59 pm is commonly called Pie Minute?

According to Wikipedia, π, in Euclidean plane geometry, is defined “either as the ratio of a circle’s circumference to its diameter, or as the ratio of a circle’s area to the area of a square whose side is the radius”. Since π is an irrational number, the exact value of π has an infinite decimal expansion and does not repeat. The first 50 decimal places of π is

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

The following is a short history of how π was calculated from Wikipedia:

• The Egyptian scribe Ahmes wrote the oldest known text to give an approximate value for π, corresponding to a value of 256 divided by 81 or 3.160.
• As early as the 19th century BC, Babylonian mathematicians were using π = 25/8, which is within 0.53% of the exact value.
• An early approximation of pi is in the Bible, 1 King 7:23. The circumference is related to the diameter with a ratio of 30 to 10, which gives an estimate of 3 for pi.
• By finding perimeters of circumscribed and inscribed regular polygons, Archimedes found that π is between 3 + 10/71 and 3 + 1/7.
• The Chinese mathematician Liu Hui computed π to 3.141014 (good to three decimal places) in AD 263 and suggested that 3.14 was a good approximation.
• According to I Ching (635–713), the Arc of 1/4 circle is 10, the chord is 9 so π = v2/0.9×2 = 3.1426968052735445.
• The Indian mathematician and astronomer Aryabhata in the 5th century gave the approximation π = 62832/20000 = 3.1416, correct when rounded off to four decimal places.
• The Chinese mathematician and astronomer Zu Chongzhi computed π to be between 3.1415926 and 3.1415927 in the 5th century.
• In the 14th century, the Indian mathematician and astronomer Madhava of Sangamagrama found a rational approximation of π that was correct to 13 decimal places of accuracy.
• In 1424, the Persian Muslim mathematician and astronomer Ghyath ad-din Jamshid Kashani (1380–1429) correctly computed 2π to 9 sexagesimal (base 60) digits. This figure is equivalent to 16 decimal (base 10) digits as 2*π = 6.2831853071795865 which corresponds to π = 3.14159265358979325.

Now with the help of supercomputers, the latest record of calculating pi is held by Professor Yasumasa Kanada of the Information Technology Center at Tokyo University. In September 2002, Kanada and his team calculated 206.158 billion places of pi using a Hitachi supercomputer for 400 hours. In October 2005, the same team claimed they have calculated pi to 1.24 trillion places.

But do we really need so many digits? Wikipedia says if we use only 10 decimal places of π to compute the circumference of the Earth’s equator from its radius, the error is less than 0.2 millimeters.

And, what’s the memory record of π? According to Memory and Mental Calculation World Records,  the verified record belongs to Chao Lu of China who recited 67,850 digits of π in 2005 (Wow).

*Photo from www.ime.uerj.br.

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