Piphilology

History

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. In 1949 a computer was used to calculate π to 2000 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. An institution from Germany provides the details of the “Pi World Ranking”; see the website at http://www.pi-world-ranking-list.com.

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 has several variations, including:

How I need a drink, alcoholic in nature, after the tough chapters involving quantum mechanics!

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 instead of one of the several roundings, 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 would know

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) learned

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.)

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

In the children's book, 'Somewhen' (David Saul and Danielle Mathieson, ISBN 9780473218584), a poem is presented as a riddle. Here, the words describe the ratio and as laid out, the riddle forms a circle. To side-step the zero at decimal position 32, the word 'nothing' is used.

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 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.

The following sonnet is a mnemonic for pi to 75 decimal places in iambic pentameter:

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.

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, slant rhyme, 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 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, known as "Pilish". For example, Poe, E.: Near a Raven represents 740 digits, Cadaeic Cadenza encodes 3835, 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 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.

Persian

خرد و دانش و آگاهی دانشمندان .ره سرمنزل مقصود بما آموزد

Translation:

The wisdom, science, and knowledge of scholars, will show us the way to destination.

Note: By counting the number of each letters in each word you are able to memorize pi to the 10th decimal place. ex: خرد (kherad) = 3, و (va) = 1, دانش (daanesh) = 4, و (va) = 1, آگاهی (aagaahi) = 5, ...

Hungarian

Nem a régi s durva közelítés, Mi szótól szóig így kijön Betűiket számlálva. Ludolph eredménye már, Ha itt végezzük húsz jegyen. De rendre kijő még tíz pontosan, Azt is bízvást ígérhetem.

Translation:

It is not the old and rough approximation, What comes out word by word Counting their letters. Ludolph's result is already here, If we do it, on twenty digits. But come out ten more precisely I also promise definitely.

An interesting (not math themed) alternative:

Bír-e, érez-e ember nyugalmat, Ha lelkét nehéz bús emlék zaklatja. Szüntelen felhőbe burkolózó idő az, Ami változni ámha akarna se tudhat, Mert azt nem írhattya már le halandó kívánsága.

Translation:

Whether has, whether feels a man a peace of mind If his soul is harassed by heavy, sad memories. The continuously clouded time is, What cannot change although it want, Because it cannot be written by a mortal's desire.

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

Kur i hyej, e kryej, sigurisht, po përtoj andaj nuk fitoj — "If I start dealing with it, I will do it, but I am lazy therefore I do not win."

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 composed of alexandrines consists of words each with a number of letters that yields π to 126 decimal places:

Que j’aime à faire apprendre un nombre utile aux sages ! Immortel Archimède, artiste ingénieur, Qui de ton jugement peut priser la valeur ? Pour moi, ton problème eut de pareils avantages. Jadis, mystérieux, un problème bloquait Tout l’admirable procédé, l’œuvre grandiose Que Pythagore découvrit aux anciens Grecs. Ô quadrature ! vieux tourment du philosophe ! Insoluble rondeur, trop longtemps vous avez Défié Pythagore et ses imitateurs. Comment intégrer l’espace plan circulaire ? Former un triangle auquel il équivaudra ? Nouvelle invention : Archimède inscrira Dedans un hexagone ; appréciera son aire, Fonction du rayon. Pas trop ne s’y tiendra : Dédoublera chaque élément antérieur ; Toujours de l’orbe calculée approchera ; Définira limite ; enfin, l’arc, le limiteur De cet inquiétant cercle, ennemi trop rebelle ! Professeur, enseignez son problème avec zèle !

Translation:

How I like to teach this number useful to the wise. Immortal Archimedes, artist, engineer, in your opinion who could estimate its value? For me, your problem had equal advantages. Long ago, mysterious, a problem blocked All the honorable process, the great work That Pythagoras revealed to the Ancient Greeks. Oh quadrature! Old philosopher's torment Unsolvable roundness, for too long you have Defied Pythagoras and his imitators. How to integrate the plain circular space? Form a triangle to which it is equivalent? New invention: Archimedes will inscribe Inside a hexagon; will appreciate its area Function of a ray. Not too much to hold onto there: Will split each previous element; Always the calculated orb will approach Will define the limit; finally, the arc, the limiter Of this disturbing circle, an enemy too rebellious Teacher, teach its problem with zeal

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:

Ἀεὶ ὁ Θεὸς ὀ Μέγας γεωμετρεῖ, τὸ κύκλου μῆκος ἵνα ὁρίσῃ διαμέτρῳ, παρήγαγεν ἀριθμὸν ἀπέραντον, καὶ ὅν, φεῦ, οὐδέποτε ὅλον θνητοὶ θὰ εὕρωσι

Translation:

The Great God applies geometry forever; To define the length of the circle using its diameter, He produced an infinite number, Which, alas, mortals will never find in its entirety.

Spanish

The following piem, giving π to 31 decimal places, is well known in Argentina:

Fue y cayó. Y queda solamente la inútil cifra con pocos destinos poderosos, tristes devenires sin el más sencillo bien. Idiota, re idiota, sabe que sus encantos son ya latosos decimales. Pobre...

Translation:

It went and it fell. And only the useless figure remains, with little powerful destinies, sad future without the simplest goodness. Idiotic, very idiotic, it knows that its charms are now boring decimals. Poor...

Another. This piem gives π (correctly rounded) to 10 decimal places. (If you prefer to not round π, then replace "cosmos" with "cielo".)

Sol y luna y mundo proclaman al eterno Autor del Cosmos.

Translation:

Sun and moon and world proclaim the eternal Author of the Cosmos. (Or "heaven", not Cosmos, if using "cielo".)

Irish

Níl i mata, a shaoi, eolaíocht nó feidhm. (7 decimal places) — "Wise one, mathematics has neither science nor use."

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."

Russian

In the Russian language, there is a well-known phrase in the reform of 1917 orthography of old tradition: "Кто и шутя, и скоро пожелаетъ «Пи» узнать число — ужѣ знаетъ." (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: "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:

"Daj, o pani, o boska Mnemozyno, pi liczbę, którą też zowią ponętnie ludolfiną, pamięci przekazać tak, by jej dowolnie oraz szybko do pomocy użyć, gdy się problemu nie da inaczej rozwiązać, pauza - to zastąpić liczbami." (35 decimal places) - "Give, the lady, the divine Mnemosyne, pi number, which also is called enticingly ludolfina memory to pass so that it freely and quickly to help you use when the problem can not be otherwise resolved, pause - (dash means nil) is replaced by the numbers."

The verse of Polish mathematician Kazimierz Cwojdziński:

„Kuć i orać w dzień zawzięcie, bo plonów niema bez trudu. Złocisty szczęścia okręcie kołyszesz … Kuć. My nie czekajmy cudu. Robota to potęga ludu." (23 decimal places) - "Hammer and plow in a day obstinately, because not fruits without trouble. Golden happiness ship rocking ... Hammering. We do not let us wait miracle. Labor is the power of the people.:" Był i jest i wieki sławionym ów będzie, który kół obwód średnicą wymierzył. (12 decimal places) — "There was, and there is, and through centuries renowned will be, who circle's circumference measured with its diameter." "Kto z woli i myśli zapragnie Pi spisać cyfry, ten zdoła" (10 decimal places) - "Who will and mind wishes Pi write the numbers, this succeed."

An occasionally seen verse related to Mundial Argentina and the Polish football team:

"Już i Lato i Deyna strzelili do bramki obcej dwa karne. Lubański dostrzegł mistrza Szarmacha, gdy on tak wypuścił cios szacha, że zdobyć musi cel gry krzyknął Gol na Mundial Argentyna." (30 decimal places). - "Already and Lato and Deyna scored two goals to foreign football goal. Lubański saw master Szarmach so when he released the hit of the check, the gain must be goal of the game shouted goal at the World Cup Argentina.

Portuguese

Cai a neve e novas ferrovias de marfim serão por casas trocadas. (11 decimal places) — "The snow falls and new ivory railroads will be exchanged by houses." Com o zero o lente reprovará os alunos. (8 decimal places) — "With zero the university professor will fail the students."

Or in Brazilian Portuguese:

Sim, é útil e fácil memorizar um número grato aos sábios. — "Yes, it's useful and easy to memorize a number dear to the wisemen." Nós e todo o mundo guardamos pi usando letra por número. — "We and all the world memorize pi using letter for number." Sou o medo e temor constante do menino vadio. — "I'm the constant fear and dread of the stray boy."

A piem written in a more poetic manner:

Sou o amor, o homem impetuoso da libido Homem que ataca mulheres atraentes, meninas pecadoras que no céu imiscuem amor, paixão, fé, desejo, tudo! Até que idolatro com as sereias pecadoras tanta fé! Esbeltas mulheres para o musculado, sereias e fêmeas pecadoras Até idolatram serpentes com ardente macho. O viril desejará as pecadoras iníquas doravante para amar.

Translation:

I am the love, The impetuous man from the libido Man who attacks attractive women, sinful maidens who on heaven intrude love, passion, faith, desire, everything! I even idolize with the mermaids so much faith! Luscious women for the brawny, sinful mermaids and females They even idolize serpents with the burning buck. The virile man will wish the sinful and the iniquitous henceforth to love.

Japanese

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:

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 hú) 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

Sen, o alan o çevre bölününce ve sonsuz rakam ile çıkan değişken dizilimli sayısın. — "You are the number with infinite digits in changing order, which is found when the circumference and the area is divided."

Czech

Sám u sebe v hlavě magického pí číslic deset mám. (nine decimal places) — "I have ten digits of magical pi in my head."

Lín a kapr u hráze prohlídli si rybáře, udici měl novou, jikrnáči neuplovou. (12 decimal places) — "Tench and carp by the dam watched the fisher. He has a new rod, fish will not escape."

Dej, ó Bože, a číslo Ludolfovo já navždy pomnu, pro větší naplnění moudrosti početní. (13 decimal places) — "Oh God, let me to remember the pi forever, for the increase of mathematical skills."

Mám ó bože ó velký pamatovat si takový cifer řad, velký slovutný Archimedes, pomáhej trápenému, dej mu moc, nazpaměť nechť odříká ty slavné sice, ale tak protivné nám, ach, číslice Ludolfovy! (30 decimal places) — "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."

Serbian

Čak i Grci i stari Vavilonci su kazali: obime kad deliš krugovim prečnikom dobijaš neophodan nam pi. (16 decimal places) — "Even Greeks and Old Babylonians have told: when dividing circumferences with circle's diameter you obtain the indispensable pi."

Italian

Non è dato a tutti ricordare il numero aureo del sommo filosofo Archimede. Certuni sostengon che si può ricordare tale numero, ma questi poi non recitano che un centone insensato. (29 decimal places) — "Not anybody can retain the golden number of the great philosopher Archimedes. There are who claim it is possible to recall this number, but then they just recite a senseless cento"

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

Even before computers calculated π, memorizing a record number of digits became an obsession for some people. The record for memorizing digits of π, certified by Guinness World Records, 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