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| {{redirect|Palindromes|the film|Palindromes (film)}}
| | == New Jordan Shoes Release == |
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| A '''palindrome''' is a word, phrase, [[palindromic number|number]], or other sequence of symbols or elements, whose meaning may be interpreted the same way in either forward or reverse direction.<ref>with general allowances for adjustments to [[punctuation]] and [[word divider]]s.</ref> Famous examples include "Amore, Roma", "A man, a plan, a canal: Panama" and "No 'x' in 'Nixon'".
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| Composing literature in palindromes is an example of [[constrained writing]]. The word "palindrome" was coined from the Greek roots ''{{lang|grc-Latn|palin}}'' ({{lang|grc|πάλιν}}; "again") and ''{{lang|grc-Latn|dromos}}'' ({{lang|grc|δρóμος}}; "way, direction") by the English writer [[Ben Jonson]] in the 17th century. The Greek phrase to describe the phenomenon is ''{{lang|grc-Latn|karkinikê epigrafê}}'' ({{lang|grc|καρκινικὴ επιγραφή}}; "[[crab]] inscription"), or simply ''karkinoi'' ({{lang|grc|καρκίνοι}}; "crabs"), alluding to the movement of crabs, such as an inscription that may be read backwards.
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| [[File:Sator Square at Oppède.jpg|thumb|right|The [[Sator Square]].]]
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| Palindromes date back at least to 79 AD, as a palindrome was found as a graffito at [[Herculaneum]], a city buried by ash in that year. This palindrome, called the [[Sator Square]], consists of a sentence written in Latin: "[[Sator Square|Sator Arepo Tenet Opera Rotas]]" ("The sower Arepo holds with effort the wheels"). It is remarkable for the fact that the first letters of each word form the first word, the second letters form the second word, and so forth. Hence, it can be arranged into a [[word square]] that reads in four different ways: horizontally or vertically from either top left to bottom right or bottom right to top left. As such, they can be referred to as palindromatic.
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| A palindrome with the same property is the [[Hebrew language|Hebrew]] palindrome, "We explained the glutton who is in the honey was burned and incinerated", (<span class="script-hebrew" style="font-size:145%; font-family:'SBL Hebrew', David, Narkisim, 'Times New Roman', 'Ezra SIL SR', FrankRuehl, 'Microsoft Sans Serif', 'Lucida Grande'" dir="rtl">פרשנו רעבתן שבדבש נתבער ונשרף</span>; perashnu: ra`avtan shebad'vash nitba'er venisraf''), by [[Abraham ibn Ezra]], referring to the [[Halacha|halachic]] question as to whether a fly landing in honey makes the honey ''[[Kashrut|treif]]'' (non-kosher).
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| {| style="font:200%/75% monospace; text-align:center;"
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| |ן||ת||ב||ע||ר
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| |ש||ב||ד||ב||ש
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| |ר||ע||ב||ת||נ
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| |ף||ר||ש||נ||ו
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| Another Latin palindrome, "''In girum imus nocte et consumimur igni''" ("We go wandering at night and are consumed by fire", in which "''In girum ire''" is translated as "go wandering" instead of the literal "go in a circle", cf. Italian "''andare in giro''", "go strolling or wandering around"), was said to describe the behavior of moths. It is likely that this palindrome is from medieval rather than ancient times.
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| [[Byzantine Empire|Byzantine Greeks]] often inscribed the palindrome, "Wash [the] sins, not only [the] face" {{lang|grc|ΝΙΨΟΝ ΑΝΟΜΗΜΑΤΑ ΜΗ ΜΟΝΑΝ ΟΨΙΝ}} ("''[[Nipson anomemata me monan opsin|Nīpson anomēmata mē mōnan ōpsin]]''", engraving "''ps''" with the single Greek letter Ψ, [[Psi (letter)|psi]]), on [[baptismal font]]s. This practice was continued in many English churches. Examples include the font at [[St. Mary's Church, Nottingham]] and also the font in the basilica of [[Hagia Sophia|St. Sophia]], [[Constantinople]], the font of St. Stephen d'Egres, [[Paris]]; at St. Menin's Abbey, [[Orléans]]; at [[Dulwich College]]; and at the following churches: [[Worlingworth]] (Suffolk), [[Harlow]] (Essex), [[Knapton]] (Norfolk), [[St Martin, Ludgate]] (London), and [[Hadleigh, Suffolk|Hadleigh]] (Suffolk).
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| ===Palindromes in Arabic language===
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| [[Arabic language]] is an [[abjad]]; that is, only [[consonant]]s are represented as [[Letter (alphabet)|letters]]. [[Vowel]]s are not visible as letters. Instead, they can be represented using [[diacritics]]. Palindromes in Arabic are taken from letters (consontants) only, disregarding vowels that follow/proceed them. Examples are shown below.
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| ====In the Quran====
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| # '''{{lang|ar|ربك فكبر}}''' ([[Romanization of Arabic|transl.:]] ''rabbaka fakabbir, [And] your Lord glorify'') ([http://quran.com/74/3 Quran 74:3]) <br> The sentence reads ''rabbaka fakabbir''. Here, reading the sentence backwards including vowels would not create a palindrome. However, taking out consonants only (which are here: '''''r''''', '''''b''''', '''''k''''', '''''f''''', '''''k''''', '''''b''''', '''''r''''') can clearly create a palindrome.
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| # '''{{lang|ar|كل فى فلك}}''' ([[Romanization of Arabic|transl.:]] ''kullun fi falak, ... [but] each, in an orbit, is swimming'') ([http://quran.com/36/40 Quran 36:40]) <br> Consontants are: '''''k''''', '''''l''''', '''''f''''', '''''y''''', '''''f''''', '''''l''''', '''''k'''''.
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| ====In Arabic literature====
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| There is a [[verse]] in a [[poem]] credited to an [[anonymous]] that is fully reversible. The verse reads:
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| :'''{{lang|ar|مودته تدوم لكل هول * وهل كل مودته تدوم}}'''
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| The verse [[Romanization of Arabic|transliterates]] to: ''mawaddatuhu tadumu likulli hawlin * wahal kullu mawaddatihi tadumu''; and [[Translation|translates]] to: ''His cordiality lasts despite all calamities * but, will all of his cordiality last?''
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| Consonants are: '''''m''''', '''''w''''', '''''d''''', '''''t''''', '''''h''''', '''''t''''', '''''d''''', '''''w''''', '''''m''''', '''''l''''', '''''k''''', '''''l''''', '''''h''''', '''''w''''', '''''[l]''''', '''''w''''', '''''h''''', '''''l''''', '''''k''''', '''''l''''', '''''m''''', '''''w''''', '''''d''''', '''''t''''', '''''h''''', '''''t''''', '''''d''''', '''''w''''', '''''m'''''; with ''[l]'' being the mid letter.
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| ===Palindromes in ancient Sanskrit===
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| Palindromes of considerable complexity were experimented with in [[Sanskrit]] poetry.<ref>Mathematical Circus, p. 250</ref> Complex palindromes appear in the 19th canto of the 8th-century epic poem [[Śiśupāla-vadha]] by [[Magha (poet)|Magha]]. It yields the same text if read forward, backward, down, up, or diagonally:
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| {| style="width:200px;"
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| | style="color:orange;" | sa- || ka- || ra- || na- || na- || ra- || ka- || style="color:red;" | sa-
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| | style="color:green;" | kā- || ya- || sā- || da- || da- || sā- || ya- || style="color:red;" | kā
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| | style="color:blue;" | ra- || sā- || ha- || vā || vā- || ha- || sā- || style="color:red;" | ra-
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| | style="color:pink;" | nā- || da- || vā- || da- || da- || vā- || da- || style="color:red;" | nā.
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| | style="color:yellow;" | (nā || da || vā || da || da || vā || da || style="color:red;" | nā
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| | style="color:orange;" | ra || sā || ha || vā || vā || ha || sā || style="color:red;" | ra
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| | style="color:blue;" | kā || ya || sā || da || da || sā || ya || style="color:red;" | kā
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| |- style="color:red;"
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| | style="color:purple;" | sa || kā || ra || nā || nā || ra || kā || style="color:red;" | sa)
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| |}
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| (Note: a hyphen indicates a continuation of same word.) The last four lines are an inversion of the first four and are not part of the verse. They are included here only so that its properties may be more easily discerned, as the up-and-down reading depends on re-reading the text back up again in each column.
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| The stanza translates as:
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| :[That army], which relished battle (''rasāhavā''), contained allies who brought low the bodes and gaits of their various striving enemies (''sakāranānārakāsakāyasādadasāyakā''), and in it the cries of the best of mounts contended with musical instruments (''vāhasāranādavādadavādanā'').
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| The same work (''[[Śiśupāla-vadha]]'') also contains stanzas in which each line is a palindrome, and stanzas that may be read backward to give a new stanza ([[#Semordnilaps|semordnilaps]]). Such stanzas are also found in the earlier work ''[[Kirātārjunīya]]''.
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| This Sanskrit poem was written by "nandi-ghanta kavis" in kanda style.
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| सारस नयना घन जघ
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| नारचित रतार कलिक हर सार रसा
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| सार रसारह कलिकर
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| तारत चिरनाघ जनघ नायनसरसा |
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| ===Palindromes in Tamil poetry===
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| Palindromes are referred to in Tamil as "Maalai Maatru" (மாலை மாற்று). The earliest known palindromic verses (11 couplets) occur in the devotional poetry of the [[Shaivite|Shaivism]] saint [[Campantar|Sambandhar]] who lived around the 7th Century C.E.
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| The first of these eleven verses runs thus:
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| யாமாமாநீ யாமாமா யாழீகாமா காணாகா
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| காணாகாமா காழீயா மாமாயாநீ மாமாயா
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| It refers to [[Shiva]] as the incomparable God, the one who plays the [[Veena (instrument)|Veena]], the beautiful one adorned with snakes, the one who destroyed [[Kama Deva, the god of Love|Kama]], whose abode is [[Sirkazhi]], who also appears as [[Vishnu]], and beseeches him (Shiva) to rid the devotee of impurities.
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| Palindromic verses are also to be found in Madhava Shivagnana Yogi's ''Kanchi Puranam'' (மாதவச்சிவஞானயோகிகள் காஞ்சிப் புராணம்) and in Mahavidvaan Meenakshi Sundaram Pillai's ''Thirunaagaik Kaaronap Puranam'' (மகாவித்துவான் மீனாட்சிசுந்தரம் பிள்ளை திருநாகைக் காரோணப் புராணம்).<ref>{{cite web|url=http://thevaaram.org/thirumurai_1/songview.php?thiru=3&Song_idField=31170&padhi=117&startLimit=0&limitPerPage=1&sortBy=&sortOrder=DESC |title=thevaaram.org |publisher=thevaaram.org |date=2007-01-25 |accessdate=2012-04-23}}</ref>
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| ===Palindromes in Persian (Farsi) ===
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| A famous example that most students in Iran have heard in literature classes is:
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| شکر بترازوی وزارت برکش
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| literally could be translated to "weigh the sugar with the ministry scale"
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| ==Types==
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| ===Character, word, or line unit===
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| The most familiar palindromes, in English at least, are character-by-character: The written characters read the same backward as forward. Some examples of common palindromic words: ''civic'', ''radar'', ''level'', ''rotor'', ''noon'', ''kayak'', ''reviver'', ''racecar'', ''redder'', ''madam'', ''[[Malayalam]]'', and ''refer''.<!-- per [[WP:INDISCRIMINATE}}, please don't add further examples just because you can; these are EXAMPLES only --> There are also palindromes where the unit of reversal is the word ("So patient a doctor to doctor a patient so") or line (as in the poem "Doppelganger" by J.A. Lindon). These are referred to as "word-unit palindromes" and "line-unit palindromes" respectively.<ref>"Never Odd Or Even, and Other Tricks Words Can Do" by O.V. Michaelsen (Sterling Publishing Company: New York), 2005 p124-7</ref> Word-unit palindromes were popularized in the [[logology|recreational linguistics]] community by J.A. Lindon in the 1960s, but occasional examples in English are found from at least the 19th century, and several in French and Latin date to the Middle Ages.<ref>{{cite web | url = http://www.kmjn.org/notes/word_unit_palindromes.html | title = Word-unit palindromes | author = Mark J. Nelson | date = 2012-02-07 | accessdate = 2012-11-18}}</ref>
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| ===Phrases===
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| Palindromes often consist of a phrase or sentence, e.g.: "Eva, can I stab bats in a cave?", "Mr. Owl ate my metal worm", "Was it a car or a cat I saw?", "A nut for a jar of tuna", "Do geese see God?", "Ma is as selfless as I am", "On a clover, if alive erupts a vast pure evil, a fire volcano." "Dammit, I'm mad!", "A Toyota's a Toyota", "Go hang a salami, I'm a lasagna hog", and "A Santa lived as a devil at NASA". Punctuation, capitalization, and spacing are usually ignored, although some, such as "Rats live on no evil star" and "Step on no pets", include the spacing.
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| ===Famous English palindromes===
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| Some well-known English palindromes are, "Able was I ere I saw [[Elba]]",<ref>Noting the first exile of [[Napoleon]] to Elba</ref> "A man, a plan, a canal - Panama!",<ref name="MercerPanama">By Leigh Mercer, published in ''Notes and Queries,'' 13 Nov. 1948, according to ''The Yale Book of Quotations,'' F. R. Shapiro, ed. (2006, ISBN 0-300-10798-6).</ref> "Madam, I'm Adam" or "Madam in Eden, I'm Adam", "Doc, note: I dissent. A fast never prevents a fatness. I diet on cod"<ref>{{cite news|title=Professor Peter Hilton|url=http://www.telegraph.co.uk/news/obituaries/science-obituaries/8124447/Professor-Peter-Hilton.html|newspaper=[[Daily Telegraph]]|accessdate=30 April 2011|location=London|date=10 November 2010}}</ref> and "Never odd or even". "Rise to vote, sir" was featured in an episode of ''[[The Simpsons]]''.
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| ===Names===
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| Some people have names that are palindromes. Included are [[given name]]s (Ada, Anna, Bob, Aviva), [[surname]]s (Harrah, Renner, Salas, Arora) or both (Eve, Hannah, Maham, Otto). [[Lon Nol]] (1913–1985) was Prime Minister of Cambodia. [[Nisio Isin]] is a Japanese novelist and [[manga]] writer, whose real name (西尾 維新, ''Nishio Ishin'') is a palindrome when romanized using the [[Kunrei-shiki]] or the [[Nihon-shiki]] systems. (It is often written as NisiOisiN to emphasize this). Some persons have changed their name in order to make of it a palindrome (one example is actor [[Robert Trebor]]), while others were given a palindromic name at birth (such as the philologist [[Revilo P. Oliver]]). Some names can be made part of a larger palindrome, like: "You have no name, Manon Eva Huoy!".
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| Palindromic names are very common in Finland. Examples include Olavi Valo, Emma Lamme, Sanna Rannas, Anni Linna and Asko Oksa.
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| There are also palindromic names in fictional media. "Stanley Yelnats" is the name of a character in ''[[Holes (novel)|Holes]]'', a 1998 novel and [[Holes (film)|2003 film]]. Four of the fictional ''[[Pokémon]]'' [[List of Pokémon|species]] have palindromic names in English ([[Eevee]], Girafarig, Ho-Oh, and Alomomola).
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| ===Molecular biology===
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| {{Main|Palindromic sequence}}
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| [[Restriction enzymes]] recognize a specific sequence of nucleotides and produce a double-stranded cut in the DNA. While recognition sequences vary widely, with lengths of between 4 and 8 nucleotides, many of them are ''palindromic'', which correspond to nitrogenous base sequences between complementary strands, which, when read from the 5' to 3' direction, are identical sequences.
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| ===Numbers===
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| {{Main|Palindromic number}}
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| A palindromic number is a number whose digits, with [[decimal]] representation usually assumed, are the same read backward, for example, 5885. They are studied in [[recreational mathematics]] where palindromic numbers with special properties are sought. A [[palindromic prime]] is a palindromic number that is a [[prime number]], for example, 191 and 313.
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| The [[continued fraction]] of <math>\sqrt{n} + \lfloor\sqrt{n}\rfloor</math> is a repeating palindrome when <math>n</math> is an integer.
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| The last palindromic year was 2002. There won't be another one until 2112.
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| ===Acoustics===
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| A palindrome in which a recorded phrase of speech sounds the same when it is played backward was discovered by composer [[John Oswald (composer)|John Oswald]] in 1974 while he was working on audio tape versions of the [[cut-up technique]] using recorded readings by [[William S. Burroughs]]. Oswald discovered in repeated instances of Burroughs speaking the phrase "I got" that the recordings still sound like "I got" when played backward.<ref>{{cite web|url=http://www.pfony.com/ |title=Section titled "On Burroughs and Burrows ..." |publisher=Pfony.com |date= |accessdate=2012-04-23}}</ref><ref>[http://www.pfony.com/burrows/index.html Reversible audio cut-ups of William S. Burroughs' voice], including an acoustic palindrome in example 5 (requires [[Adobe Flash|Flash]])</ref>
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| In France, a more complex example has been identified with{{Citation needed|date=August 2011}}
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| "Une slave valse nue"
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| ''(a Slavic girl waltzes naked)''.
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| ====Classical music====
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| [[Joseph Haydn]]'s [[Symphony No. 47 (Haydn)|Symphony No. 47]] in G is nicknamed "the Palindrome". The third movement, [[minuet]] and [[trio (music)|trio]] is a musical palindrome. The second half of the piece is the same as the first but backwards.
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| The interlude from [[Alban Berg]]'s opera ''[[Lulu (opera)|Lulu]]'' is a palindrome, as are sections and pieces, in [[arch form]], by many other composers, including [[James Tenney]], and most famously [[Béla Bartók]]. [[George Crumb]] also used musical palindrome to text paint the [[Federico García Lorca]] poem "¿Por qué nací?", the first movement of three in his fourth book of [[Madrigal (music)|Madrigal]]s. [[Igor Stravinsky]]'s final composition, ''The Owl and the Pussy Cat'', is a palindrome.{{Citation needed|date=October 2011}}
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| The first movement from [[Constant Lambert]]'s [[ballet]] ''[[Horoscope (ballet)|Horoscope]]'' (1938) is entitled "Palindromic Prelude". Lambert claimed that the theme was dictated to him by the ghost of [[Bernard van Dieren]], who had died in 1936.<ref>{{cite web|url=http://www.answers.com/topic/horoscope-ballet |title=Answers.com |publisher=Answers.com |date= |accessdate=2012-04-23}}</ref>
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| British composer [[Robert Simpson (composer)|Robert Simpson]] also composed music in the palindrome or based on palindromic themes; the slow movement of his [[Symphony No. 2 (Simpson)|Symphony No. 2]] is a palindrome, as is the slow movement of his [[String Quartet No. 1 (Simpson)|String Quartet No. 1]]. His hour-long [[String Quartet No. 9 (Simpson)|String Quartet No. 9]] consists of thirty-two variations and a fugue on a palindromic theme of Haydn (from the minuet of his Symphony No. 47). All of Simpson's thirty-two variations are themselves palindromic.
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| The music of [[Anton Webern]] is often palindromic. Webern, who had studied the music of the Renaissance composer [[Heinrich Isaac]], was extremely interested in symmetries in music, be they horizontal or vertical. An example of horizontal or linear symmetry in Webern's music is the first phrase in the second movement of the [[symphony]], Op. 21. A striking example of vertical symmetry is the second movement of the [[Variations for piano (Webern)|Piano Variations]], Op. 27, in which Webern arranges every pitch of this [[dodecaphonic]] work around the central pitch axis of A4. From this, each downward reaching interval is replicated exactly in the opposite direction. For example, a G{{Music|sharp}}3—13 half-steps down from A4 is replicated as a B{{Music|flat}}5—13 half-steps above.
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| Just as the letters of a verbal palindrome are not reversed, so are the elements of a musical palindrome usually presented in the same form in both halves. Although these elements are usually single notes, palindromes may be made using more complex elements. For example, [[Karlheinz Stockhausen]]'s composition ''[[Mixtur]]'', originally written in 1964, consists of twenty sections, called "moments", which may be [[Permutation|permuted]] in several different ways, including retrograde presentation, and two versions may be made in a single program. When the composer revised the work in 2003, he prescribed such a palindromic performance, with the twenty moments first played in a "forwards" version, and then "backwards". Each moment, however, is a complex musical unit, and is played in the same direction in each half of the program.<ref>Rudolf Frisius, ''Karlheinz Stockhausen II: Die Werke 1950–1977; Gespräch mit Karlheinz Stockhausen, "Es geht aufwärts"'' (Mainz, London, Berlin, Madrid, New York, Paris, Prague, Tokyo, Toronto: Schott Musik International, 2008): 164–65. ISBN 978-3-7957-0249-6.</ref> By contrast, [[Karel Goeyvaerts]]'s 1953 electronic composition, ''[[Nummer 5]] (met zuivere tonen)'' is an ''exact'' palindrome: not only does each event in the second half of the piece occur according to an axis of symmetry at the centre of the work, but each event itself is reversed, so that the note attacks in the first half become note decays in the second, and vice-versa. It is a perfect example of Goeyvaerts's aesthetics, the perfect example of the imperfection of perfection.<ref>M[orag] J[osephine] Grant, ''Serial Music, Serial Aesthetics: Compositional Theory in Post-war Europe'' (Cambridge, U.K.; New York: Cambridge University Press, 2001): 64–65.</ref>
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| In [[classical music]], a [[crab canon]] is a [[canon (music)|canon]] in which one line of the melody is reversed in time and pitch from the other.
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| A large-scale musical palindrome covering more than one movement is called "chiasic", referring to the cross-shaped Greek letter "[[Chi (letter)|χ]]" (pronounced /ˈkaɪ/.) This is usually a form of reference to the crucifixion; for example, the ''{{lang|la|[[Mass in B minor structure#Crucifixus|Crucifixus]]}}'' movement of Bach's [[Mass in B minor]]. The purpose of such palindromic balancing is to focus the listener on the central movement, much as one would focus on the center of the cross in the crucifixion. Other examples are found in Bach's cantata BWV 4, ''[[Christ lag in Todesbanden, BWV 4|Christ lag in Todesbanden]]'', Handel's ''[[Messiah (Handel)|Messiah]]'' and the [[Requiem (Fauré)|Fauré Requiem]].<ref>{{cite book |author=Charton, Shawn E. |title=Jennens vs. Handel: Decoding the Mysteries of Messiah }}</ref>
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| A [[table canon]] is a rectangular piece of sheet music intended to be played by two musicians facing each other across a table with the music between them, with one musician viewing the music upside down compared to the other. The result is somewhat like two speakers simultaneously reading the [[Sator square]] from opposite sides, except that it is typically in two-part polyphony rather than in unison.
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| ====Popular music====
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| =====Musical content=====
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| [[Hüsker Dü]]'s concept album ''[[Zen Arcade]]'' contains the songs, "Reoccurring Dreams" and "Dreams Reoccurring", the latter of which appears earlier on the album, but is actually the [[Introduction (music)|intro]] of the former song played in reverse. In a similar manner, [[The Stone Roses]]' [[The Stone Roses (album)|first album]] contains the songs "[[Waterfall (The Stone Roses song)|Waterfall]]" and "Don't Stop", the latter of which is, in essence, the former performed backward. The 12" and CD formats of their single [[Elephant Stone]] feature the B-side "Full Fathom Five", which is an alternate mix of the title track played in reverse.
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| The title track of the 1992 album entitled ''[[UFO Tofu]]'' by [[Béla Fleck and the Flecktones]] is said by its composer to be a musical palindrome.
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| In 2003, the city of [[San Diego, California]] commissioned sculptor Roman DeSalvo and composer [[Joseph Waters]] to create a public artwork in the form of a safety railing on the 25th Street overpass at F and 25th Streets. The result, ''Crab Carillon'', is a set of 488 tuned chimes that may be played by pedestrians as they cross the overpass. Each chime is tuned to the note of a melody, composed by Waters. The melody is in the form of a palindrome, to accommodate walking in either direction.<ref>{{cite web|url=http://web.archive.org/web/20071031095814/http://www.sandiego.gov/arts-culture/installations.shtml |title=City of San Diego Public Art website |publisher=Web.archive.org |date=2007-10-31 |accessdate=2012-04-23}}</ref>
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| The strings part in "[[Starálfur]]", from the album ''[[Ágætis byrjun]]'' by [[Sigur Rós]], is a palindrome.
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| The song "[[You Can Call Me Al]]" by [[Paul Simon]] features a palindromic [[bass run]] performed by [[Bakithi Kumalo]].
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| =====Lyrics=====
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| The song, "[[I Palindrome I]]", by [[They Might Be Giants]], features palindromic lyrics and imagery. The 27-word bridge is word-symmetrical.
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| [["Weird Al" Yankovic]]'s song, "[[Bob ("Weird Al" Yankovic song)|Bob]]", from his 2003 album ''[[Poodle Hat]]'', consists of rhyming palindromes and is a style parody the [[Bob Dylan]] song "[[Subterranean Homesick Blues]]". There is an accompanying video for the song which also parodies Dylan's video. Yankovic shows all of the palindromes on cue cards as they are being sung.
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| [[Baby Gramps]] is known for songs where the lyrics are made up of palindromes.
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| =====Names and titles=====
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| [[ABBA]]'s song "[[SOS (ABBA song)|SOS]]" is the only [[Billboard Hot 100]] single to have both a title and a recording artist whose names are both palindromes.
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| The [[Grateful Dead]]'s 1969 album ''[[Aoxomoxoa]]'' is a notable early use of a palindrome in the title of a popular music album.
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| In 1992, the [[grunge]] band [[Soundgarden]] released an [[extended play|EP]] called ''[[Satanoscillatemymetallicsonatas]]'' or ''SOMMS''; the title is a palindrome and puns on the supposed connection between [[the Devil]] and [[heavy metal music|heavy metal]] music.
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| On [[Boris (band)|Boris]] and [[Sunn O)))]]'s collaborative album "[[Altar (Sunn O))) and Boris album)|Altar]]", the vinyl version included a full disc, double-sided bonus track entitled "Satan Oscillate My Metallic Sonatas" (in reference to the Soundgarden EP of the same name), in which the various instruments (mainly guitars) are introduced one at a time on side one, and then fade out in reverse order on side two. Kim Thayil of Soundgarden appears on this track.
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| [[The Fall of Troy]] made a song with the famous palindrome "A Man, A Plan, A Canal, Panama" as the title.
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| The first and last tracks on [[Andrew Bird]]'s album ''[[Noble Beast]]'' form a palindrome ("Oh No" and "On Ho!") and the seventh track is a palindrome in itself: "Ouo". He has also mentioned palindromes in earlier music, giving his songs names such as "11:11", "T'N'T", and "Fake Palindromes" (although the last title is not a palindrome itself). He also mentions palindromes in the lyrics of the song "I" and the "I" redux "Imitosis".
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| "racEcar" by [[Vitamin Party]] features a repeating chorus of "A Man, A Plan, A Canal, Panama" (the title itself is palindromic).
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| "Never Odd or Even", which was to be the title of the first album by [[Aleka's Attic]], the band formed by the late [[River Phoenix]], is a palindrome.<ref>{{cite web|url=http://www.river-phoenix.org/music/chapter5/ |title=Rio's Attic - Phoenix Music |publisher=River-phoenix.org |date= |accessdate=2012-04-23}}</ref>
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| "Neveroddoreven" (or "Never Odd or Even") is the title of an album by [[Shonlock]], released in 2011. This palindrome is stylized on the album's cover as "NEVERODⱭOЯƎVƎИ". This album also contains the song "Never Odd or Even".
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| "[[If I Had a Hi-Fi]]", a 2010 cover album by American alternative rock band [[Nada Surf]], is a palindrome.
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| [[Miles Davis]] and [[Black Sabbath]] both had albums called ''Live Evil''. Inversely, [[Lynch Mob]] and [[Diamond Head (band)|Diamond Head]] had albums called ''Evil Live''.
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| [[D.R.U.G.S.]] has two songs that are palindromes on the self-titled debut album, "Mr. Owl Ate My Metal Worm" and "[[Laminated E.T. Animal]]".
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| In 2009, rock band "Dopapod" released an album entitled "I Saw Live Dopapod Evil Was I".
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| The Asian-American teenage Riot Grrrl band [[Emily's Sassy Lime]]'s name is palindromic.
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| In 2012, the American band [[Liars (band)|Liars]] released an LP called [[WIXIW]].
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| The German electronic trio [[To Rococo Rot]] is also a palindrome.
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| ====Comics====
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| [[Watchmen]] #5, "Fearful Symmetry", the first page mirrors the last (in terms of frame disposition), with the following pages mirroring each other before the center-spread is (broadly) symmetrical in layout.
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| "NogegoN", Volume 3 of ''Les Terres creuses'', by Luc et [[François Schuiten]], Les Humanoïdes Associés, (1990) : each frame has its mirror image.
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| ====Television====
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| [[Disney]]'s ''[[Phineas and Ferb]]'' frequently alludes to palindromes, including the once-mentioned character Professor Ross E. Forp. Danville, the setting locale is also said to have a "Palindrome Road".
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| ==Long palindromes==
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| The longest palindromic word in the Oxford English Dictionary is the [[Onomatopoeia|onomatopoeic]] ''tattarrattat'', coined by [[James Joyce]] in ''[[Ulysses (novel)|Ulysses]]'' (1922) for a knock on the door. The ''Guinness Book of Records'' gives the title to ''detartrated'', the [[preterite]] and past participle of ''detartrate'', a chemical term meaning to remove [[tartrate]]s. [[Rotary tiller|Rotavator]], a trademarked name for an agricultural machine, is often listed in dictionaries. The term ''redivider'' is used by some writers, but appears to be an invented or derived term—only ''redivide'' and ''redivision'' appear in the Shorter Oxford Dictionary. ''[[Malayalam]]'', an Indian language, is of equal length.
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| In English, two palindromic novels have been published: ''Satire: Veritas'' by David Stephens (1980, 58,795 letters), and ''Dr Awkward & Olson in Oslo'' by Lawrence Levine (1986, 31,954 words).<ref>{{cite book |author=Eckler, Ross |title=Making the Alphabet Dance |publisher=St. Martin's |location=NY |year=1996 |page=36 |isbn=0-333-90334-X }}</ref> In French, [[Oulipo]] writer [[Georges Perec]]'s "Grand Palindrome" (1969) is 5,556 letters in length.<ref>{{cite book |author=Perec, Georges |title=La Littérature Potentielle, idées |publisher=Gallimard |location=Paris |year=1973 }}</ref><ref>{{cite book |author=Bellos, David |title=Georges Perec: A Life in Words |publisher=David R. Godine |location=NY |page=429 |isbn=0-87923-980-8 }}</ref> In Hebrew, Noam Dovev wrote a 1,001-word, 3,773 letter palindromic story called, "Name sold, I'd lose man".<ref>{{cite journal |author=Dovev, Noam |title=Name sold, I'd lose man |journal=Palindromic blog |date=2013-02-12 |url=http://hebrewpalindrome.wordpress.com/2013/02/12/הפלינדרום-הארוך-ביותר-בעברית}}</ref><ref>{{cite web|publisher=Haaretz newspaper |author=Arad, Roy Chicky |title=Palindrome - How can you read it? |date=2013-02-28 |url=http://www.haaretz.co.il/news/education/1.1940711}}</ref>
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| ==Biological structures==
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| {{Main|Palindromic sequence}}
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| [[File:DNA palindrome.svg|thumb|600px|right|Palindrome of [[DNA structure]]<br>A: Palindrome, B: Loop, C: Stem]]
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| In most [[genome]]s or sets of [[gene]]tic instructions, palindromic motifs are found. The meaning of palindrome in the context of genetics is slightly different, however, from the definition used for words and sentences. Since the [[DNA]] is formed by two paired strands of [[nucleotides]], and the nucleotides always pair in the same way ([[Adenine]] (A) with [[Thymine]] (T), [[Cytosine]] (C) with [[Guanine]] (G)), a (single-stranded) sequence of DNA is said to be a palindrome if it is equal to its complementary sequence read backward. For example, the sequence <tt>ACCTAGGT</tt> is palindromic because its complement is <tt>TGGATCCA</tt>, which is equal to the original sequence in reverse complement.
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| A palindromic [[DNA]] sequence may form a [[stem-loop|hairpin]]. Palindromic motifs are made by the order of the [[nucleotide]]s that specify the complex chemicals ([[protein]]s) that, as a result of those [[genetics|genetic]] instructions, the [[cell (biology)|cell]] is to produce. They have been specially researched in [[bacteria]]l chromosomes and in the so-called Bacterial Interspersed Mosaic Elements (BIMEs) scattered over them. Recently{{when|date=January 2011}} a research genome sequencing project discovered that many of the bases on the [[Y chromosome|Y-chromosome]] are arranged as palindromes.{{Citation needed|date=January 2009}} A palindrome structure allows the Y-chromosome to repair itself by bending over at the middle if one side is damaged.
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| It is believed that palindromes frequently are also found in proteins,<ref name="aac">{{cite journal |author=Ohno S |title=Intrinsic evolution of proteins. The role of peptidic palindromes |journal=[[Riv. Biol.]] |volume=83 |issue=2-3 |pages=287–91, 405–10 |year=1990 |pmid=2128128}}</ref><ref name="ac">{{cite journal |doi=10.1023/A:1023454111924 |author=Giel-Pietraszuk M, Hoffmann M, Dolecka S, Rychlewski J, Barciszewski J |title=Palindromes in proteins |journal=J. Protein Chem. |volume=22 |issue=2 |pages=109–13 |date=February 2003 |pmid=12760415 |url=http://www.kluweronline.com/art.pdf?issn=0277-8033&volume=22&page=109}}</ref> but their role in the protein function is not clearly known. It has recently<ref name="am">{{cite journal |author=Sheari A, Kargar M, Katanforoush A, ''et al.'' |title=A tale of two symmetrical tails: structural and functional characteristics of palindromes in proteins |journal=BMC Bioinformatics |volume=9 |page=274 |year=2008 |pmid=18547401 |pmc=2474621 |doi=10.1186/1471-2105-9-274 |url=http://www.biomedcentral.com/1471-2105/9/274}}</ref> been suggested that the prevalence existence of palindromes in peptides might be related to the prevalence of low-complexity regions in proteins, as palindromes frequently are associated with low-complexity sequences. Their prevalence might also be related to an [[alpha helical]] formation propensity of these sequences,<ref name="am"/> or in formation of proteins/protein complexes.<ref name="X">{{cite journal |author=Pinotsis N, Wilmanns M |title=Protein assemblies with palindromic structure motifs |journal=Cell. Mol. Life Sci. |volume=65 |issue=19 |pages=2953–6 |date=October 2008 |pmid=18791850 |doi=10.1007/s00018-008-8265-1}}</ref>
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| ==Computation theory==
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| In the [[automata theory]], a [[set (mathematics)|set]] of all palindromes in a given [[alphabet]] is a typical example of a [[formal language|language]] that is [[context-free language|context-free]], but not [[Regular language|regular]]. This means that it is impossible for a [[finite automaton|computer with a finite amount of memory]] to reliably test for palindromes. (For practical purposes with modern computers, this limitation would apply only to incredibly long letter-sequences.)
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| In addition, the set of palindromes may not be reliably tested by a [[deterministic pushdown automaton]] which also means that they are not [[LR parser|LR(k)-parsable]] or [[LL parser|LL(k)-parsable]]. When reading a palindrome from left-to-right, it is, in essence, impossible to locate the "middle" until the entire word has been read completely.
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| It is possible to find the [[longest palindromic substring]] of a given input string in [[linear time]].<ref name=Jewels>{{citation
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| | last1 = Crochemore | first1 = Maxime
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| | last2 = Rytter | first2 = Wojciech | author2-link = Wojciech Rytter
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| | title = Jewels of Stringology: Text Algorithms
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| | publisher = World Scientific
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| | year = 2003
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| | isbn = 978-981-02-4897-0
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| | contribution = 8.1 Searching for symmetric words
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| | pages = 111–114}}</ref><ref>{{citation
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| | last = Gusfield | first = Dan
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| | contribution = 9.2 Finding all maximal palindromes in linear time
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| | doi = 10.1017/CBO9780511574931
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| | isbn = 0-521-58519-8
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| | location = Cambridge
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| | mr = 1460730
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| | pages = 197–199
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| | publisher = Cambridge University Press
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| | title = Algorithms on Strings, Trees, and Sequences
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| | year = 1997}}</ref>
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| The '''palindromic density''' of an infinite word ''w'' over an alphabet ''A'' is defined to be zero if only finitely many prefixes are palindromes; otherwise, letting the palindromic prefixes be of lengths ''n''<sub>''k''</sub> for ''k''=1,2,... we define the density to be
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| :<math> d_P(w) = \left( { \limsup_{k \rightarrow \infty} \frac{n_{k+1}}{n_k} } \right)^{-1} \ . </math>
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| Among aperiodic words, the largest possible palindromic density is achieved by the [[Fibonacci word]], which has density 1/φ, where φ is the [[Golden ratio]].<ref name=AB443>{{citation | last1=Adamczewski | first1=Boris | last2=Bugeaud | first2=Yann | chapter=8. Transcendence and diophantine approximation | editor1-last=Berthé | editor1-first=Valérie | editor2-last=Rigo | editor2-first=Michael | title=Combinatorics, automata, and number theory | location=Cambridge | publisher=[[Cambridge University Press]] | series=Encyclopedia of Mathematics and its Applications | volume=135 | page=443 | year=2010 | isbn=978-0-521-51597-9 | zbl=pre05879512 }}</ref>
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| A '''palstar''' is a composition of palindromic strings.<ref name=Jewels/>
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| {{anchor|Semordnilaps}}
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| ==Semordnilap==
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| ''Semordnilap'' is a name coined for a word or phrase that spells a ''different'' word or phrase backward. "semordnilap" is itself "palindromes" spelled backward. According to logologist Dmitri A. Borgmann,<ref>{{cite book |author=Borgmann, Dmitri A. |title=Language on Vacation |publisher=Charles Scribner's Sond |location=NY |year=1965 |page=42}}</ref> the word was coined by Martin Gardner in ''Oddities and Curiosities of Words and Literature''.<ref>{{cite book |author=Bombaugh, C. C. | editor=Gardner, Martin|title=Oddities and Curiosities of Words and Literature |year=1961|page=345 }}</ref> Semordnilaps are also known as volvograms,<ref>{{cite web|url=http://www3.merriam-webster.com/opendictionary/newword_search.php?word=volvogram |title=Merriam-Webster's Open Dictionary |publisher=.merriam-webster.com |date=2005-09-26 |accessdate=2012-04-23}}</ref> heteropalindromes, semi-palindromes, half-palindromes, reversgrams, mynoretehs, reversible anagrams,<ref>{{cite web|url=http://www.oxforddictionaries.com/page/wordbackwards |title=AskOxford: What is the word for a word that is another word spelt backwards? |publisher=Oxforddictionaries.com |date= |accessdate=2012-04-23}}</ref> word reversals, or anadromes.<ref name="anagrammy">{{cite web|url=http://www.anagrammy.com/anagrams/faq3.html |title=Anagrams FAQ Page - Are there any unusual varieties of anagram? |publisher=Anagrammy.com |date=2011-03-19 |accessdate=2012-04-23}}</ref> They have also sometimes been called antigrams,<ref name="anagrammy"/> though now, this term usually refers to anagrams with opposing meanings.
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| These words are very useful in constructing palindromic texts; together, each pair forms a palindrome, and they may be added on either side of a shorter palindrome in order to extend it.
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| The longest single-word English examples contain eight letters, such as "stressed" ("desserts") and "dioramas" ("samaroid", resembling a [[samara (fruit)|samara]]). Other shorter examples include "deliver" ("reviled") and "swap" ("paws").
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| ==Non-English palindromes==
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| According to Guinness World Records, the [[Finnish language|Finnish]] word ''saippuakivikauppias'' ([[soapstone]] vendor), a 19-letter word, is claimed to be the world's longest palindromic word in everyday use. A meaningful derivative from it is ''saippuakalasalakauppias'' (soapfish bootlegger). An even longer effort is ''saippuakuppinippukauppias'' ([[soap dish]] wholesale vendor), albeit somewhat contrived in its meaning. The proper name "Otto Nenonen" is often combined with the previous noun(s), making the name-title combination an even longer phrase. Almost equally long is the [[Estonian language|Estonian]] word ''kuulilennuteetunneliluuk'' (the hatch a bullet flies out of when exiting a tunnel).
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| The longest palindrome in the Dutch language, according to the ''Dutch Guinness Book of World Records'', is ''koortsmeetsysteemstrook'', which translates into English as ''strip of a fever measurement system''.<ref>{{cite web | url=https://nl.wikipedia.org/wiki/Palindroom | title=Wikipedia De vrije encyclopedie | publisher=Wikimedia Foundation, Inc. | date=2013-12-17 | accessdate=2013-12-21}}</ref>
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| ==See also==
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| *[[Ambigram]]
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| *[[Anagram]]
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| *[[Antimetabole]]
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| *[[Backmasking]]
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| *[[Constrained writing]]
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| *[[List of palindromic places]]
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| *[[Palindromic number]]
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| *[[Palindromic polynomial]]
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| *[[Pangram]]
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| *[[Phonetic palindrome]]
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| *[[Su Hui (poet)]]
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| *[[Yreka, California]] for the palindromic ''Yreka Bakery'' and ''Yrella Gallery''
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| ==References==
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| {{Reflist|30em}}
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| ==External links==
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| {{Wiktionary|palindrome|Appendix:Palindromic words}}
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| {{Wikiquote}}
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| {{Commons category|Palindromes}}
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| * [http://www.poetandknowit.com/english-definitions/palindrome-examples.aspx List of palindromes from Princeton Lexical Database.]
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| {{Hidden messages}}
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| [[Category:Constrained writing]]
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| [[Category:Palindromes| ]]
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| [[Category:Word games]]
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