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Piphilology comprises the creation and use of mnemonic techniques to remember a span of digits of the mathematical constant Ï. The word is a play on Pi itself and the linguistic field of philology.
There are many ways to memorize Ï, including the use of piems (a portmanteau, formed by combining pi and poem), which are poems that represent Ï in a way such that the length of each word (in letters) represents a digit. Here is an example of a piem: How I need a drink, alcoholic of course [or, in nature] after the heavy lectures involving quantum mechanics. Notice how the first word has 3 letters, the second word has 1, the third has 4, the fourth has 1, the fifth has 5, and so on. In longer examples, 10-letter words are used to represent the digit zero, and this rule is extended to handle repeated digits in so-called Pilish writing. The Cadaeic Cadenza records the first 3834 digits of Ï in this manner, and a 10,000-word novel, Not A Wake, has now been composed accordingly.[1]
However, piems prove inefficient for large memorizations of pi. Other methods include remembering patterns in the numbers (for instance, the year 1971 appears in the first fifty digits of pi) and the method of loci (used to memorize Ï to 65,536 digits).[2]
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Until the 20th century, the number of digits of pi which mathematicians have had the stamina to calculate by hand remained in the hundreds, so that memorization of all known digits at the time was possible.[4] In 1949 a computer was used to calculate Ï to 2000 places, presenting one of the earliest opportunities for a more difficult challenge.
Subsequent computers calculated pi to extraordinary numbers of digits (2.7 trillion as of August, 2010)[5] , and people began memorizing more and more of the output. The world record for the number of digits memorized has exploded since mid-century, and stands at 100,000 as of October 2006.[6] The previous record (83,431) was set by the same person (Akira Haraguchi) on July 2, 2005,[7] and the record previous to that (42,195) was held by Hiroyuki Goto. An institution from Germany provides the details of the âPi World Rankingâ; see the website at http://www.pi-world-ranking-list.com.
The most common mnemonic technique is to memorize a so-called "piem" (play on pi and poem) in which the number of letters in each word is equal to the corresponding digit of Ï. This famous example has several variations, including:
Short mnemonics such as these, of course, do not take one very far down Ï's infinite road. Rather, they are intended more as amusing doggerel. If even less accuracy suffices, the following examples can be used:
This second one gives the value of Ï as 3.141592653, while the first only brings it to the second "5". Indeed, many published piems use truncation instead of one of the several roundings, thereby producing a less accurate result when the first omitted digit is greater than or equal to 5. It is advantageous to use truncation in memorizing if the individual intends to study more places later on, otherwise one will be remembering erroneous digits.
Another mnemonic is:
In this mnemonic the word "point" represents the decimal point itself.
Yet another example is:
In this example, the spelling of Archimedes is altered so that it represents 9.
Longer mnemonics employ the same concept. This example created by Peter M. Brigham incorporates twenty decimal digits:
Some mnemonics, such as this poem which gives the "3." and the first 20 decimal digits, use the separation of the poem's title and main body to represent the decimal point:
Another, more poetic version is:
A 30-digit extension of the same proceeds as follows:
There are minor variations on the above rhyme, which still allow pi to be worked out correctly. However, one variation replaces the word "lexicon's" with "lesson's" and in doing so, incorrectly indicates that the 18th digit is 7.
The logologist Dmitri Borgmann gives the following 30-word poem in his book, Language on vacation: An olio of orthographical oddities:[8]
The following sonnet is a mnemonic for pi to 75 decimal places in iambic pentameter:
Note that in this example, 10-letter words are used to represent the digit zero.
There are piphilologists who have written texts that encode hundreds or thousands of digits. This is an example of constrained writing, known as "Pilish". For example, Poe, E.: Near a Raven[9] represents 740 digits, Cadaeic Cadenza encodes 3835, and Not A Wake[10] extends to 10,000 digits.
It is also possible to use the rhythm and sound of the spoken digits themselves as a memorization device. The mathematician John Horton Conway composed the following arrangement for the first 100 digits,
_ _ _
3 point 1415 9265 35
^ ^
_ _ _ _ _ _ __
8979 3238 4626 4338 3279
** **^^ ^^ ****
. _ _ __ _ _ _ . _ .
502 884 197 169 399 375 105 820 974 944
^ ^ ^ ^
59230 78164
_ _ _ _
0628 6208 998 6280
^^ ^^ ^^
.. _ .._
34825 34211 70679,
^ ^
where the accents indicate various kinds of repetition.[11]
Translation:
An interesting (not math themed) alternative:
Translation:
Another alternative:
This statement yields Ï to nine decimal places:
English translation that doesn't encode pi:
Looser English translation that encodes pi:
The following statement and question consists of words each with a number of letters that yields Ï to 126 decimal places:
Translation:
An alternative beginning:
Yielding Ï to 22 decimal places:
Translation:
The following piem, giving Ï to 31 decimal places, is well known in Argentina:
Translation:
Another. This piem gives Ï (correctly rounded) to 10 decimal places. (If you prefer to not round Ï, then replace "cosmos" with "cielo".)
Translation:
NÃl i mata, a shaoi, eolaÃocht nó feidhm. (7 decimal places) â "Wise one, mathematics has neither science nor use."
In the Russian language, there is a well-known phrase in the pre-1917-reform orthography of old tradition: "ÐÑо и ÑÑÑÑ, и ÑкоÑо пожелаеÑÑ Â«Ðи» ÑзнаÑÑ ÑиÑло â Ñжѣ знаеÑÑ." (The one who would wish to know the number Pi easily and quickly, already knows it.)
A more modern rhyme is:
A short approximation is: "ЧÑо Ñ Ð·Ð½Ð°Ñ Ð¾ кÑÑÐ³Ð°Ñ ?" (What do I know about circles?)
In addition, there are several non-folklore verses that simply rhyme the digits of Pi "as is"; for examples, see the Russian version of this article.
ByÅ i jest i wieki sÅawionym ów bÄdzie, który kóŠobwód ÅrednicÄ wymierzyÅ. (13 decimal places) â "There was, and there is, and through centuries renowned will be, who circle's circumference measured with its diameter."
Or in Brazilian Portuguese:
A piem written in a more poetic manner:
Translation:
Japanese piphilology has countless mnemonics based on punning words with numbers. This is especially easy in Japanese because there are two or three ways to pronounce each digit, and the language has relatively few phonemes to begin with. For example, to 31 decimal places:[12]
| 身 | ä¸ã¤ | ä¸ | ä¸ã¤ | ç | ã | ã« | ç¡ | æ | å³ | ã | ã | ã | 㪠| ã | 身 | ãµ | ã¿ | ã | èª | ã | ä¼¼ | ã | ã | ãã | ãã | é | ã« | 㪠| ã | |
| 3. | 1 | 4 | 1 | 5 | 9 | 2 | 6 | 5 | 3 | 5 | 8 | 9 | 7 | 9 | 3 | 2 | 3 | 8 | 4 | 6 | 2 | 6 | 4 | 3 | 3 | 8 | 3 | 2 | 7 | 9 |
| mi | hitotsu | yo | hitotsu | iku | ni | mu-imi | iwakunaku | mi | fumiya | yomu | niro | yo | san | zan | yami | ni | naku | |||||||||||||
This is close to being ungrammatical nonsense, but a loose translation prioritizing word order yields:
Japanese children also use songs built on this principle to memorize the multiplication table.
It is possible to construct piphilogical poems in Chinese by using homophones or near-homophones of the numbers zero through nine, as in the following well known example which covers 22 decimal places of Ï. In this example the character meaning "mountain" (å±± shÄn) is used to represent the number "three" (ä¸ sÄn), the character meaning "I" (å¾ wú) is used to represent the number "five" (äº wÇ), and the characters meaning "temple" (寺 sì) and "die" (æ» sÇ) are used to represent the number "four" (å sì). Some of the mnemonic characters used in this poem, for example "kill" (殺 shÄ) for "three" (ä¸ sÄn), "jug" (壺 hú) for "five" (äº wÇ), "happiness" (æ¨ lè) for "six" (å liù) and "eat" (å chÄ«) for "seven" (ä¸ qÄ«), are not very close phonetically in Mandarin Chinese.
| å±± | å· | ä¸ | 寺 | ä¸ | 壺 | é |
| shÄn | diÄn | yÄ« | sì | yÄ« | hú | jiÇ |
| 3 | . | 1 | 4 | 1 | 5 | 9 |
| ç¾ | æ¨ | è¦ | ç | å¾ | ||
| Är | lè | kÇ | shÄ | wú | ||
| 2 | 6 | 5 | 3 | 5 | ||
| æ | é | å | é | 殺 | ç¾ | |
| bÇ | jiÇ | chÄ« | jiÇ | shÄ | Är | |
| 8 | 9 | 7 | 9 | 3 | 2 | |
| 殺 | ä¸ | æ» | æ¨ | ç¾ | æ¨ | |
| shÄ | bù | sÇ | lè | Är | lè | |
| 3 | 8 | 4 | 6 | 2 | 6 |
This can be translated as:
Sen, o alan o çevre bölününce ve sonsuz rakam ile çıkan deÄiÅken dizilimli sayısın. â "You are the number with infinite digits in changing order, which is found when the circumference and the area is divided."
Sám u sebe v hlavÄ magického pà ÄÃslic deset mám. (9 decimal places) â "I have ten digits of magical Pi in my head."
LÃn a kapr u hráze prohlÃdli si rybáÅe, udici mÄl novou, jikrnáÄi neuplovou. (12 decimal places) â "Tench and carp by the dam watched the fisher. He has a new rod, fish will not escape."
Dej, ó Bože, a ÄÃslo Ludolfovo já navždy pomnu, pro vÄtÅ¡Ã naplnÄnà moudrosti poÄetnÃ. (13 decimal places) â "Oh God, let me to remember the Pi forever, for the increase of mathematical skills."
Mám ó bože ó velký pamatovat si takový cifer Åad, velký slovutný Archimedes, pomáhej trápenému, dej mu moc, nazpamÄÅ¥ nechÅ¥ odÅÃká ty slavné sice, ale tak protivné nám, ach, ÄÃslice Ludolfovy! (30 decimal places) â "Shall I, God oh almighty, remember such a long string of numbers, great and famous Archimedes, help my careworn being, give me the power, to recite by heart all the digits, which may be famous, but also hated by some of us, the digits of Ludolph van Ceulen."
AÅa e bine a scrie renumitul Åi utilul numÄr. (8 decimal places) â "This is the way to write the renowned and useful number."
Äak i Grci i stari Vavilonci su kazali: obime kad deliÅ¡ krugovim preÄnikom dobijaÅ¡ neophodan nam Pi. (16 decimal places) â "Even Greeks and Old Babylonians have told: when dividing circumferences with circle's diameter you obtain the indispensable Pi."