Happy Pi Day courtesy of Richard Green.

Happy Pi Day courtesy of Richard Green. 

This post reminds me of the memory palace memorization technique. You can read/learn more here:

The Secrets of Sherlock’s Mind Palace via Smithsonian.com

http://goo.gl/LxeaFR

TED talk, Feats of memory anyone can do

http://goo.gl/N2k5fl

#ScienceEveryday  

Originally shared by Richard Green

How to remember 100,000 digits of pi

The retired Japanese engineer Akira Haraguchi (1946–) claims to hold the world record for reciting the most memorized digits of the number pi. He set the record starting at 9am on October 3, 2006, and reached digit number 100,000 at 1.28am on October 4, 2006. 

The event was filmed in a public hall near Tokyo. Haraguchi took 5-minute breaks to eat every two hours, and even his trips to the toilet were filmed to prove that the feat was genuine. This broke Haraguchi’s previous record of 83,431 digits, which he performed from July 1–2, 2005.

The reason I say that Haraguchi claims to hold the record is that, for some reason, the Guinness World Records organization has failed to recognize this achievement, despite the existence of witnesses and detailed documentation. The Guinness-recognized record for reciting pi is 67,890 digits by Lu Chao, a 24-year-old graduate student from China, who recited the digits, without error, in 24 hours and 4 minutes.

Haraguchi’s technique for memorizing long lists of numbers is quite interesting. He assigns kana characters to each number, each of which represents a Japanese syllable. In his system, the digit 0 can be read as o, ra, ri, ru, re, ro, wo, on or oh; the digit 1 can be read as a, i, u, e, hi, bi, pi, an, ah, hy, hyan, bya, or byan; and there are analogous rules for the other digits.

Using this system, Haraguchi has created many stories and poems, including a story about the 12th century hero Minamoto no Yoshitsune. The first 15 digits of pi, which are 3.14159265358979, are rendered in Haraguchi’s system as the words saishi ikokuni mukosan kowakunaku, whose approximate meaning is “the wife and children have gone abroad; the husband is not scared.”

Given all this, it may be surprising to learn that as a child, Haraguchi was neither a prodigy nor a mathematical genius. On the contrary, one of his teachers once made him stand to attention in the hallway as a punishment for badly failing to memorize multiplication tables of one-digit numbers.

Relevant links

Akira Haraguchi: http://en.wikipedia.org/wiki/Akira_Haraguchi

Minamoto no Yoshitsune: http://en.wikipedia.org/wiki/Minamoto_no_Yoshitsune

The Kana writing system: http://en.wikipedia.org/wiki/Kana

A 2006 article from the Japan Times about Haraguchi: http://goo.gl/d4H2pB

It looks as if the article’s URL may change at some point, so you may want to Google the article’s title instead: How can anyone remember 100,000 numbers?

The web site http://pi-world-ranking-list.com/ maintains a list of records of reciting from memory digits of the irrational numbers pi, e, and the square root of 2.

Picture credit: Travis Morgan

Picture source and associated poem: https://www.flickr.com/photos/morgantj/5575500301/in/photolist

#mathematics #piday  

Ramanujan and Pi

Ramanujan and Pi

Happy Pi Day courtesy of Richard Green. I wonder what Ramanujan would have accomplished, had he lived longer than 32 years.

Originally shared by Richard Green

Happy Pi Day!

The number pi or π (approximately 3.14159265) is well known as the ratio of the circumference of a circle to its diameter. Although π is an irrational number, meaning that it cannot be expressed exactly as a fraction, it is possible to express the number as an infinite series. 

One of the simplest such series is π = 4 – (4/3) + (4/5) – (4/7) + (4/9) – (4/11)… The standard techniques of calculus can be used to prove that this series converges to π. Unfortunately, the convergence is very slow, meaning that one needs to write down a large number of terms to approximate π with any degree of accuracy.

The Indian mathematician Srinivasa Ramanujan (1887-1920) found some approximations to π that are much better than the above series. The formula for the infinite series at the bottom of the picture is due to Ramanujan. It converges so quickly that each successive term in the series computes a further eight decimal places of π. To give you some idea of how accurate the formula is, the approximation given by just one term is 9801/(sqrt(8)x1103), which works out as about 3.14159273001. This is accurate to eight significant figures, and has the first six decimal places correct!

This is a very impressive approximation from a mathematician who worked before the era of computers. Perhaps not surprisingly, Ramanujan’s contemporaries were curious about where he got his ideas. The answer is quite interesting: while dreaming, he received visions of scrolls of complex mathematical content from his family goddess, Mahalakshmi of Namakkal.

Although he died at the age of 32, Ramanujan left behind a large number of mathematical results, and some of the best modern methods for computing π are based on his work. Ramanujan did not write up proofs for many of his results, although most of them turned out to be both correct and original. However, he left behind four famous notebooks of rough ideas, one of which was lost until 1976. These notebooks have inspired many papers by later mathematicians attempting to prove Ramanujan’s results.

Relevant links

The Wikipedia page on approximations to π: http://en.wikipedia.org/wiki/Approximations_of_%CF%80

The Wikipedia page on Srinivasa Ramanujan: http://en.wikipedia.org/wiki/Srinivasa_Ramanujan

A popular post by Malthus John from Halloween 2013, showing the first infinite series I mentioned, carved into a pumpkin: https://plus.google.com/102744407669548081722/posts/frJVPykwpWV

A popular post by me from August 2013 about π, featuring the digital art of Cristian Ilies Vasile: https://plus.google.com/101584889282878921052/posts/8AFefDCfV4h

(Disclaimer: I am from the UK, where March 14th is 14.3, not 3.14. Call me irrational, but I don’t think that pi day is a real thing.)

#mathematics #scienceeveryday