piphilology piphilology piphilology comprises the creation and use of mnemonic techniques to remember many digits of the mathematical constant π. the word is a play on the word "pi" itself and of the linguistic field of philology. part of a series of articles on themathematical constant π 3.1415926535897932384626433... uses area of a circle circumference use in other formulae properties irrationality transcendence value less than 22/7 approximations madhava's correction term memorization people archimedes liu hui zu chongzhi aryabhata madhava jamshīd al-kāshī ludolph van ceulen françois viète seki takakazu takebe kenko william jones john machin william shanks srinivasa ramanujan john wrench chudnovsky brothers yasumasa kanada history chronology a history of pi in culture indiana pi bill pi day related topics squaring the circle basel problem six nines in π other topics related to π there are many ways to memorize π, including the use of piems (a portmanteau, formed by combining pi and poem), which are poems that represent π in a way such that the length of each word (in letters) represents a digit. here is an example of a piem: "now i need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics." notice how the first word has three letters, the second word has one, the third has four, the fourth has one, the fifth has five, 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 short story "cadaeic cadenza" records the first 3,834 digits of π 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 π. other methods include remembering patterns in the numbers (for instance, the year 1971 appears in the first fifty digits of π) and the method of loci (which has been used to memorize π to 67,890 digits). history recent decades have seen a surge in the record number of digits memorized. until the 20th century, the number of digits of pi which mathematicians 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. 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 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 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: sir, i send a rhyme excelling, in sacred truth and rigid spelling, numerical sprites elucidate, for me the lexicon's full weight, if nature gain, who can complain, tho' dr johnson fulminate? sir, i bear a rhyme excelling in mystic force and magic spelling celestial sprites elucidate all my own striving can't relate or locate they who can cogitate and so finally terminate. finis. 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. 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 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 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 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. 0 1 2 3 4 5 6 7 8 9 - s, z, soft c d, t, th n m r l j, sh, soft ch, dg, zh, soft g k, hard c, hard g, q, qu v, f b, p vowel sounds, w, h, y (no value) examples in other languages persian خرد | و | دانش | و | آگاهی | دانشمندان .ره | سرمنزل | مقصود | بما | آموزد wisdom, science, and the knowledge of scholars, will show us the way to the destination. counting the letters in each word (additionally separated by "|") gives 10 decimal places of π: 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. 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