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EspañolPIPHILOLOGY
'Piphilology' comprises the creation and use of mnemonic techniques to remember a span of digits of the mathematical constant π. The word is a play on Pi itself and the linguistic field of philology. Even before computers calculated π, memorizing a record number of digits became an obsession for some people. The current world record is 100,000 decimal places, set on October 3 2006 by Akira Haraguchi.
There are many ways to memorise π, including the use of 'piems', 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: ''How I need a drink, alcoholic of course, 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. The Cadaeic Cadenza contains the first 3834 digits of π in this manner. 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).
Until the 20th century, the number of digits of pi which mathematicians had had the stamina to calculate by hand remained in the hundreds, so that memorization of ''all'' known digits at the time was possible.[1] In 1949 a computer was used to calculate π to 2000 places, presenting one of the earliest opportunities for a difficult challenge.
Subsequent computers calculated pi to extraordinary numbers of digits (more than a trillion as of 2006), 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.[2] The previous record (83,431) was set by the same person (Akira Haraguchi) on July 2, 2005,[3] and the record previous to that (42,195) was held by Hiroyuki Goto.
The most common mnemonic technique is to memorize a sentence in which the number of letters in each word is equal to the corresponding digit of π. The most famous example has several variations, including:
:# ''How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!''
:# ''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. Rather, 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!''
:# ''Can I have a large container of coffee? Thank you.''
This second one gives the value of π as 3.141592653, although 3.141592654 is a more correct figure. Indeed, many published 'piem's use truncation instead of one of the several roundings, thereby producing a less accurate result when the first omitted digit is greater than 5. It is advantageous to use truncation in memorising if the individual intends to study more places later on.
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.
Longer mnemonics employ the same concept. This example created by Peter M. Brigham, can be used for 21 or fewer digits:
:''How I wish I could enumerate pi easily, since all these bullshit mnemonics prevent recalling any of pi's sequence more simply.''
Some mnemonics, such as this poem which gives the first 20 digits, use the separation of the poem's title and main body to represent the decimal point (note that the word remember has 8 letters instead of 9):
: ''Pie''
: ''I wish I could remember pi''
: ''Eureka, cried the great inventor''
: ''Christmas pudding, Christmas pie''
: ''Is the problem's very center.''
Another, more poetic 30 digit version is:
:''Sir, I send a rhyme excelling,''
:''In sacred truth and rigid spelling,''
:''Numerical sprites elucidate,''
:''For me the lexicon's dull weight,''
:''If nature gain, not you complain''
:''Tho' Dr Johnson fulminate.''
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 following sonnet is a mnemonic for pi 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.''
There are piphilologists who have written poems encoding hundreds of digits. This is an example of constrained writing. See ''Poe, E.: Near a Raven''[4] for an extreme example, and Cadaeic Cadenza for an even more extreme one.
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. [5]
The following statement and question consists of words each with a number of letters that yields π to 126 decimal places:
:Que j'aime à faire apprendre ce 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 would like to learn this number useful to the wise.
:Immortal Archimedes, artist, engineer,
:in your opinion who could estimate its value?
:...
Alternative:
: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 !
:...
Yielding π to 22 decimal places:
:Ἀεὶ ὁ Θεὸς ὀ Μέγας γεωμετρεί,
:τὸ κύκλου μήκος ίνα ορίση διαμέτρω,
:παρήγαγεν ἀριθμόν ἀπέραντον,
:καὶ ὄν, φεύ, ουδέποτε ὄλον θνητοὶ θὰ εὔρωσι
Translation:
:Always the great God uses Geometry;
:So that he could define the perimeter of the circle using its diameter,
:He produced a number everlasting,
:Which, alas, mortals will never find in its entirety.
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...
In the Russian language, there is a well-known phrase in the pre-1917-reform 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:
:;Это я знаю и помню прекрасно,
::I know the following and remember it perfectly,
:;Пи многие знаки мне лишни, напрасны.
::Multitudes of the digits of Pi are unnecessary and idle for me.
A short approximation is: "Что я знаю о кругах?" (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 .
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:[6]
:
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.
★ Feynman point
★ Cadaeic Cadenza
★ Remembering the digits of ''e''
1. A history of Pi
2. (broken link)
3. Japanese breaks pi memory record
4. "Poe, E.: Near a Raven", Mike Keith's World of Words & Numbers
5. "Math Forum » Discussions » History » math-history-list", Math Forum
6. 暗記法 Japanese mnemonics for π (and some other languages as well)
{{wikiquote|English mathematics mnemonics#Pi|
★ Andreas P. Hatzipolakis: ''PiPhilology''. A site with hundreds of examples of mnemonics for π
★ Memorize 1000 digits of pi
★ Memorise 300 digits of pi
There are many ways to memorise π, including the use of 'piems', 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: ''How I need a drink, alcoholic of course, 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. The Cadaeic Cadenza contains the first 3834 digits of π in this manner. 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).
| Contents |
| History |
| Examples in English |
| Examples in other languages |
| French |
| Ancient Greek |
| Spanish |
| Russian |
| Japanese |
| See also |
| Notes and references |
| External links |
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 had the stamina to calculate by hand remained in the hundreds, so that memorization of ''all'' known digits at the time was possible.[1] In 1949 a computer was used to calculate π to 2000 places, presenting one of the earliest opportunities for a difficult challenge.
Subsequent computers calculated pi to extraordinary numbers of digits (more than a trillion as of 2006), 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.[2] The previous record (83,431) was set by the same person (Akira Haraguchi) on July 2, 2005,[3] and the record previous to that (42,195) was held by Hiroyuki Goto.
Examples in English
The most common mnemonic technique is to memorize a sentence in which the number of letters in each word is equal to the corresponding digit of π. The most famous example has several variations, including:
:# ''How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!''
:# ''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. Rather, 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!''
:# ''Can I have a large container of coffee? Thank you.''
This second one gives the value of π as 3.141592653, although 3.141592654 is a more correct figure. Indeed, many published 'piem's use truncation instead of one of the several roundings, thereby producing a less accurate result when the first omitted digit is greater than 5. It is advantageous to use truncation in memorising if the individual intends to study more places later on.
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.
Longer mnemonics employ the same concept. This example created by Peter M. Brigham, can be used for 21 or fewer digits:
:''How I wish I could enumerate pi easily, since all these bullshit mnemonics prevent recalling any of pi's sequence more simply.''
Some mnemonics, such as this poem which gives the first 20 digits, use the separation of the poem's title and main body to represent the decimal point (note that the word remember has 8 letters instead of 9):
: ''Pie''
: ''I wish I could remember pi''
: ''Eureka, cried the great inventor''
: ''Christmas pudding, Christmas pie''
: ''Is the problem's very center.''
Another, more poetic 30 digit version is:
:''Sir, I send a rhyme excelling,''
:''In sacred truth and rigid spelling,''
:''Numerical sprites elucidate,''
:''For me the lexicon's dull weight,''
:''If nature gain, not you complain''
:''Tho' Dr Johnson fulminate.''
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 following sonnet is a mnemonic for pi 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.''
There are piphilologists who have written poems encoding hundreds of digits. This is an example of constrained writing. See ''Poe, E.: Near a Raven''[4] for an extreme example, and Cadaeic Cadenza for an even more extreme one.
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. [5]
Examples in other languages
French
The following statement and question consists of words each with a number of letters that yields π to 126 decimal places:
:Que j'aime à faire apprendre ce 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 would like to learn this number useful to the wise.
:Immortal Archimedes, artist, engineer,
:in your opinion who could estimate its value?
:...
Alternative:
: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 !
:...
Ancient Greek
Yielding π to 22 decimal places:
:Ἀεὶ ὁ Θεὸς ὀ Μέγας γεωμετρεί,
:τὸ κύκλου μήκος ίνα ορίση διαμέτρω,
:παρήγαγεν ἀριθμόν ἀπέραντον,
:καὶ ὄν, φεύ, ουδέποτε ὄλον θνητοὶ θὰ εὔρωσι
Translation:
:Always the great God uses Geometry;
:So that he could define the perimeter of the circle using its diameter,
:He produced a number everlasting,
: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...
Russian
In the Russian language, there is a well-known phrase in the pre-1917-reform 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:
:;Это я знаю и помню прекрасно,
::I know the following and remember it perfectly,
:;Пи многие знаки мне лишни, напрасны.
::Multitudes of the digits of Pi are unnecessary and idle for me.
A short approximation is: "Что я знаю о кругах?" (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 .
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:[6]
:
| 身 | 一つ | 世 | 一つ | 生 | く | に | 無 | 意 | 味 | い | わ | く | な | く | 身 | ふ | み | や | 読 | む | 似 | ろ | よ | さん | ざん | 闇 | に | な | く | |
| 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:
:''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.
See also
★ Feynman point
★ Cadaeic Cadenza
★ Remembering the digits of ''e''
Notes and references
1. A history of Pi
2. (broken link)
3. Japanese breaks pi memory record
4. "Poe, E.: Near a Raven", Mike Keith's World of Words & Numbers
5. "Math Forum » Discussions » History » math-history-list", Math Forum
6. 暗記法 Japanese mnemonics for π (and some other languages as well)
External links
{{wikiquote|English mathematics mnemonics#Pi|
★ Andreas P. Hatzipolakis: ''PiPhilology''. A site with hundreds of examples of mnemonics for π
★ Memorize 1000 digits of pi
★ Memorise 300 digits of pi
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psst.. try this: add to faves
