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Piphilology comprises the creation and use of
mnemonic A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and image ...
techniques to remember many digits of the mathematical constant . The word is a play on the word "pi" itself and of the linguistic field of
philology Philology () is the study of language in oral and written historical sources; it is the intersection of textual criticism, literary criticism, history, and linguistics (with especially strong ties to etymology). Philology is also defined as ...
. There are many ways to memorize , including the use of ''piems'' (a
portmanteau A portmanteau word, or portmanteau (, ) is a blend of wordszero 0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by Multiplication, multiplying digits to the left of 0 by th ...
, and this rule is extended to handle repeated digits in so-called
Pilish Pilish is a style of constrained writing in which the lengths of consecutive words match the digits of the number ( pi). The shortest example is any three-letter word, such as "pie", but many longer examples have been constructed, including sent ...
writing. The short story "
Cadaeic Cadenza "Cadaeic Cadenza" is a 1996 short story by Mike Keith. It is an example of constrained writing, a story with restrictions on how it can be written. It is also one of the most prodigious examples of piphilology, being written in "pilish". The wo ...
" records the first 3,834 digits of in this manner, and a 10,000-word novel, ''Not A Wake'', has been written accordingly. However, poems prove to be inefficient for large memorizations of . Other methods include remembering patterns in the numbers (for instance, the year 1971 appears in the first fifty digits of ) and the method of loci (which has been used to memorize to 67,890 digits).


History

Until the 20th century, the number of digits of pi which
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
s had the stamina to calculate by hand remained in the hundreds, so that memorization of ''all'' known digits at the time was possible. In 1949 a computer was used to calculate π to 2,000 places, presenting one of the earliest opportunities for a more difficult challenge. Later computers calculated pi to extraordinary numbers of digits (2.7 trillion as of August 2010), and people began memorizing more and more of the output. The world record for the number of digits memorized has exploded since the mid-1990s, and it stood at 100,000 as of October 2006. The previous record (83,431) was set by the same person ( Akira Haraguchi) on July 2, 2005, and the record previous to that (42,195) was held by
Hiroyuki Goto recited pi from memory to 42,195 decimal places at NHK Broadcasting Centre, Tokyo on 18 February 1995. This set the world record at the time, which was held for more than a decade until Lu Chao beat it in 2005. He is a game designer at Namco. ...
. An institution from Germany provides the details of the "Pi World Ranking".


Examples in English

The most common mnemonic technique is to memorize a so-called "piem" (a wordplay on "pi" and "poem") in which the number of letters in each word is equal to the corresponding digit of π. This famous example for 15 digits has several variations, including: :''How I want a drink, alcoholic of course, after the heavy chapters involving quantum mechanics!'' - Sir James Hopwood Jeans Short mnemonics such as these, of course, do not take one very far down π's infinite road. Instead, they are intended more as amusing doggerel. If even less accuracy suffices, the following examples can be used: :''How I wish I could recollect pi easily today!'' :''May I have a large container of coffee, cream and sugar?'' This second one gives the value of π as 3.1415926535, while the first only brings it to the second five. Indeed, many published poems use
truncation In mathematics and computer science, truncation is limiting the number of digits right of the decimal point. Truncation and floor function Truncation of positive real numbers can be done using the floor function. Given a number x \in \mathb ...
instead of one of the several
rounding Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $ with $, the fraction 312/937 with 1/3, or the expression with . Rounding is often done to ob ...
s, thereby producing a less-accurate result when the first omitted digit is greater than or equal to five. 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: : ''The point I said a blind Bulgarian in France could see'' In this mnemonic the word "point" represents the decimal point itself. Yet another example is: :''How I wish I could recollect, of circle round, the exact relation Arkimedes (or Archimede) unwound.'' In this example, the spelling of Archimedes is normalised to nine. Although 'Archimedes' is, today, a more correct spelling of the ancient Greek mathematician's name in English, Archimede is also often seen when this mnemonic is given, since Archimède is the more correct spelling in some languages, such as French. This mnemonic also contains a rounding error because the digit represented by the last word "Arkimedes" (9) in 3.141592653589 is followed by 7 in π, which would cause the last two digits to round up. Longer mnemonics employ the same concept. This example created by Peter M. Brigham incorporates twenty decimal digits: :''How I wish I could enumerate pi easily, since all these bullshit mnemonics prevent recalling any of pi's sequence more simply.''


Poems

Some mnemonics, such as this poem which gives the three and the first 20 decimal digits, use the separation of the poem's title and main body to represent the decimal point: : ''Pie'' : ''I wish I could determine pi'' : ''Eureka, cried the great inventor'' : ''Christmas pudding, Christmas pie'' : ''Is the problem's very center.'' Another, more poetic version is: :''Sir, I have a rhyme excelling,'' :''In mystic power and magic spelling,'' :''Celestial spirits elucidate,'' :''For my own problems can't relate.'' Extensions to 30 or 31 decimals of the same proceed 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 seven. The logologist
Dmitri Borgmann Dmitri Alfred Borgmann (October 22, 1927 – December 7, 1985) was a German-American author best known for his work in recreational linguistics. Early life Borgmann was born on October 22, 1927, in Berlin, Germany, to Hans and Lisa Borgmann. Fe ...
gives the following 30-word poem in his book, '' Language on Vacation: An Olio of Orthographical Oddities'': :''Now, a moon, a lover refulgent in flight,'' :''Sails the black silence's loneliest ellipse.'' :''Computers use pi, the constant, when polite,'' :''Or gentle data for sad tracking aid at eclipse.'' In the fantasy book, ''Somewhen'' by David Saul, a 35-word piem both provides a description of the constant pi and the digits. The text is also laid out as a circle to provide another clue to the readers as to the purpose of the poem. In this example, the word "nothing" is used to represent the digit zero.
:''It's a fact'' :''A ratio immutable'' :''Of circle round and width,'' :''Produces geometry's deepest conundrum.'' :''For as the numerals stay random,'' :''No repeat lets out its presence,'' :''Yet it forever stretches forth.'' :''Nothing to eternity.''
The following
sonnet A sonnet is a poetic form that originated in the poetry composed at the Court of the Holy Roman Emperor Frederick II in the Sicilian city of Palermo. The 13th-century poet and notary Giacomo da Lentini is credited with the sonnet's inventio ...
is a mnemonic for pi to 75 decimal places in
iambic pentameter Iambic pentameter () is a type of metric line used in traditional English poetry and verse drama. The term describes the rhythm, or meter, established by the words in that line; rhythm is measured in small groups of syllables called " feet". "Iam ...
: :''Now I defy a tenet gallantly'' :''Of circle canon law: these integers'' :''Importing circles' quotients are, we see,'' :''Unwieldy long series of cockle burs'' :''Put all together, get no clarity;'' :''Mnemonics shan't describeth so reformed'' :''Creating, with a grammercy plainly,'' :''A sonnet liberated yet conformed.'' :''Strangely, the queer'st rules I manipulate'' :''Being followéd, do facilitate'' :''Whimsical musings from geometric bard.'' :''This poesy, unabashed as it's distressed,'' :''Evolvéd coherent - a simple test,'' :''Discov'ring poetry no numerals jarred.'' Note that in this example, 10-letter words are used to represent the digit
zero 0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by Multiplication, multiplying digits to the left of 0 by th ...
. Other poems use sound as a mnemonic technique, as in the following poem which rhymes with the first 140 decimal places of pi using a blend of
assonance Assonance is a resemblance in the sounds of words/syllables either between their vowels (e.g., ''meat, bean'') or between their consonants (e.g., ''keep, cape''). However, assonance between consonants is generally called ''consonance'' in America ...
,
slant rhyme Slant can refer to: Bias *Bias or other non- objectivity in journalism, politics, academia or other fields Technical * Slant range, in telecommunications, the line-of-sight distance between two points which are not at the same level * Slant ...
, and perfect rhyme: :''dreams number us like pi. runes shift. nights rewind'' :''daytime pleasure-piles. dream-looms create our id.'' :''moods shift. words deviate. needs brew. pleasures rise.'' :''time slows. too late? wait! foreign minds live in'' :''us! quick-minds, free-minds, minds-we-never-mind,'' :''unknown, gyrate! neuro-rhymes measure our '' :''minds, for our minds rhyme. crude ego-emanations'' :''distort nodes. id, (whose basic neuro-spacetime rhymes),'' :''plays its tune. space drones before fate unites'' :''dreams’ lore to unsung measures. whole dimensions'' :''gyrate. new number-games donate quick minds &'' :''weave through fate’s loom. fears, hopes, digits, or devils'' :''collide here—labor stored in gold-mines, lives, lightcone-'' :''piles. fate loops through dreams & pleasure-looms….'' Note that "dreams number us like pi" corresponds to "314159," and so on. Sound-based mnemonic techniques, unlike pilish, do not require that the letters in each word be counted in order to recall the digits of pi. However, where sound-based mnemonics use assonance, extra care must be taken to distinguish "nine" and "five," which contain the same vowel sound. In this example, the author assumes the convention that
zero 0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by Multiplication, multiplying digits to the left of 0 by th ...
is often called "O."


Piku

The piku follows the rules of conventional haiku (three lines of 5, 7 and 5 syllables), but with the added mnemonic trick that each word contains the same number of letters as the numerals of pi, e.g. :''How I love a verse'' :''Contrived to unhusk dryly'' :''One image nutshell''


Songs

In 2004, Andrew Huang wrote a song that was a mnemonic for the first fifty digits of pi, titled "I am the first 50 digits of pi". The first line is: :''Man, I can’t - I shan’t! - formulate an anthem where the words comprise mnemonics, dreaded mnemonics for pi.'' In 2013, Huang extended the song to include the first 100 digits of pi, and changed the title to "Pi Mnemonic Song".


Lengthier works

There are piphilologists who have written texts that encode hundreds or thousands of digits. This is an example of
constrained writing Constrained writing is a literary technique in which the writer is bound by some condition that forbids certain things or imposes a pattern. Constraints are very common in poetry, which often requires the writer to use a particular verse form. ...
, known as "
Pilish Pilish is a style of constrained writing in which the lengths of consecutive words match the digits of the number ( pi). The shortest example is any three-letter word, such as "pie", but many longer examples have been constructed, including sent ...
". For example, ''Poe, E.: Near a Raven'' represents 740 digits, ''
Cadaeic Cadenza "Cadaeic Cadenza" is a 1996 short story by Mike Keith. It is an example of constrained writing, a story with restrictions on how it can be written. It is also one of the most prodigious examples of piphilology, being written in "pilish". The wo ...
'' encodes 3,835, and ''Not A Wake'' extends to 10,000 digits.


Sound-based mnemonics

It is also possible to use the rhythm and sound of the spoken digits themselves as a memorization device. The mathematician
John Horton Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches ...
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. Another mnemonic system used commonly in the memorization of pi is the Mnemonic major system, where single numbers are translated into basic sounds. A combination of these sounds creates a word, which can then be translated back into numbers. When combined with the Method of loci, this becomes a very powerful memorization tool.


Examples in other languages


Persian

Counting the letters in each word (additionally separated by ", ") gives 10 decimal places of : خرد (kherad) = 3, و (va) = 1, دانش (daanesh) = 4, و (va) = 1, آگاهی (aagaahi) = 5, ...


Hungarian

An interesting (not math themed) alternative: Another alternative: :Íme a szám: a görög periféria pi betűje. :Euler meg Viète végtelen összeggel közelít értékéhez. :Lám, őt már Egyiptom, Kína, Európa is akarta, hogy :„ama kör kerülete úgy ki lehetne számlálva”.


Albanian


German

This statement yields π to twenty-two decimal places: :Wie, o dies π macht ernstlich so vielen viele Müh. Lernt immerhin, Mägdelein, leichte Verselein, wie so zum Beispiel dies dürfte zu merken sein. English translation that doesn't encode pi: :How, oh this π seriously makes so many struggles to so many. Learn at least, girls, simple little verses, just such as this one should be memorizable. Looser English translation that encodes pi: :Woe! O this π makes seriously so muchly many's woe.


French

The following
poem Poetry (derived from the Greek '' poiesis'', "making"), also called verse, is a form of literature that uses aesthetic and often rhythmic qualities of language − such as phonaesthetics, sound symbolism, and metre − to evoke meaning ...
composed of s consists of words each with a number of letters that yields π to 126 decimal places: An alternative beginning: :Que j’aime à faire apprendre un nombre utile aux sages ! :Glorieux Archimède, artiste ingénieur, :Toi de qui Syracuse aime encore la gloire, :Soit ton nom conservé par de savants grimoires ! :...


Katharevousa (archaizing) Greek

Yielding π to 22 decimal places:


Spanish

The following piem, giving π to 31 decimal places, is well known in
Argentina Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country in the southern half of South America. Argentina covers an area of , making it the List of South American countries by area, second-largest ...
: Another. This piem gives π (correctly rounded) to 10 decimal places. (If you prefer to not round π, then replace "cosmos" with "cielo".)


Irish

(7 decimal places)


Romanian

One of the Romanian versions of Pi poems is: There is another phrase known in Romanian that will help to memorize the number by eight decimal places: ''Așa e bine a scrie renumitul și utilul număr.'' — "This is the way to write the renowned and useful number." Another alternative for 15 decimal places:
''Ion a luat o carte, biografie, în latina veche. Are cinci capitole originale clasice latinești. —'' "Ion has bought a book, a biography, in old latin. It has five classical original latin chapters."


Russian

In the
Russian language Russian (russian: русский язык, russkij jazyk, link=no, ) is an East Slavic language mainly spoken in Russia. It is the native language of the Russians, and belongs to the Indo-European language family. It is one of four living E ...
, there is a well-known phrase in the reform of 1917
orthography An orthography is a set of conventions for writing a language, including norms of spelling, hyphenation, capitalization, word breaks, emphasis, and punctuation. Most transnational languages in the modern period have a writing system, and ...
of old tradition: A more modern rhyme is: A short approximation is: "Что я знаю о кругах?" (What do I know about circles?) In addition, there are several nonfolklore verses that simply rhyme the digits of pi "as is"; for examples, see the Russian version of this article.


Polish

The verse of Polish mathematician Witold Rybczyński (35 decimal places): (Note that the dash stands for zero.) The verse of Polish mathematician Kazimierz Cwojdziński (23 decimal places): (12 decimal places): (10 decimal places) An occasionally seen verse related to Mundial Argentina and the Polish football team (30 decimal places):


Portuguese

(11 decimal places) (8 decimal places) Or in Brazilian Portuguese: A piem written in a more poetic manner:


Japanese

Japanese piphilology has countless mnemonics based on
pun A pun, also known as paronomasia, is a form of word play that exploits multiple meanings of a term, or of similar-sounding words, for an intended humorous or rhetorical effect. These ambiguities can arise from the intentional use of homophoni ...
ning 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
phoneme In phonology and linguistics, a phoneme () is a unit of sound that can distinguish one word from another in a particular language. For example, in most dialects of English, with the notable exception of the West Midlands and the north-wes ...
s to begin with. For example, to 31 decimal places: : This is close to being ungrammatical nonsense, but a loose translation prioritizing word order yields: :''A person is one; the world is one:'' :''to live this way, it's meaningless, one says, and cries,'' :''"step on it, will ya!" then reads—be the same!'' :''Crying uncontrollably in the dark.'' Japanese children also use songs built on this principle to memorize the multiplication table.


Chinese

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 π. In this example the character meaning "mountain" (山 ''shān'') is used to represent the number "three" (三 ''sān''), the character meaning "I" (吾 ''wú'') is used to represent the number "five" (五 ''wǔ''), and the characters meaning "temple" (寺 ''sì'') and "die" (死 ''sǐ'') are used to represent the number "four" (四 ''sì''). Some of the mnemonic characters used in this poem, for example "kill" (殺 ''shā'') for "three" (三 ''sān''), "jug" (壺 ''
In Hopi and Zuni dance rituals, Hú, also known as Huhuwa and Tithu, is the Kachina of the hummingbird. The hummingbird was, and is, an important bird in puebloan cultures. Hopi legend speaks of the hummingbird as intervening on behalf of the Hopi ...
'') for "five" (五 ''wǔ''), "happiness" (樂 ''lè'') for "six" (六 ''liù'') and "eat" (吃 ''chī'') for "seven" (七 ''qī''), are not very close phonetically in Mandarin/Putonghua. : This can be translated as: :''On a mountain top a temple and a jug of wine.'' :''Your happiness makes me so bitter;'' :''Take some wine and drink, the wine will kill you;'' :''If it does not kill you, I will rejoice in your happiness.''


Turkish


Czech

(nine decimal places) (12 decimal places) (13 decimal places) (30 decimal places)


Serbian

(16 decimal places)


Italian

(30 decimal places) (10 decimal places) Chi è nudo e crepa limonando la tubera, lieto lui crepa


Sanskrit

The Katapayadi System of verses is basically a system of code so that things can be defined in a way so that people can remember. The code is as follows: With the above key in place, Sri Bharathi Krishna Tirtha in his Vedic Mathematics gives the following verse: गोपी भाग्य मधुव्रात श्रुङ्गिशो दधिसन्धिग , खलजीवित खाताव गलहालारसंधार , If we replace the code from the above table in the above verse, here is what we get. 31 41 5926 535 89793 23846 264 33832792 That gives us π/10=0.31415926535897932384626433832792


Slovene

The following piem gives π to 30 decimal places.


Memorization record holders

Even before
computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations ( computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These prog ...
s calculated , memorizing a record number of digits became an obsession for some people. The record for memorizing digits of , certified by ''
Guinness World Records ''Guinness World Records'', known from its inception in 1955 until 1999 as ''The Guinness Book of Records'' and in previous United States editions as ''The Guinness Book of World Records'', is a reference book published annually, listing world ...
'', is 70,000 digits, recited in India by Rajveer Meena in 9 hours and 27 minutes on 21 March 2015. On October 3, 2006, Akira Haraguchi, a retired Japanese engineer, claimed to have recited 100,000 decimal places, but the claim was not verified by Guinness World Records. David Fiore was an early record holder for pi memorization. Fiore's record stood as an American record for more than 27 years, which remains the longest time period for an American recordholder. He was the first person to break the 10,000 digit mark. Suresh Kumar Sharma holds Limca Book of Records for the most decimal places of pi recited by memory. He rattled off 70,030 numbers in 17 hours 14 minutes on October 21, 2015.


See also

* Mnemonist *
Cadaeic Cadenza "Cadaeic Cadenza" is a 1996 short story by Mike Keith. It is an example of constrained writing, a story with restrictions on how it can be written. It is also one of the most prodigious examples of piphilology, being written in "pilish". The wo ...
*
Memory sport Memory sport, sometimes referred to as competitive memory or the mind sport of memory, refers to competitions in which participants attempt to memorize then recall different forms of information, under certain guidelines. The sport has been formall ...


Notes and references


External links


Pi World Ranking ListTools for Piphilologist

Collection of Mnemonic Devices
{{Math mnemonics Pi Science mnemonics nl:Pi (wiskunde)#Geheugensteuntjes en dergelijke