A palindrome is a word, phrase, number or other sequence of units that has the property of reading the same in either direction (the adjustment of punctuation and spaces between words is generally permitted). A palindromic number or numeral palindrome is a 'symmetrical' number like 16461 that remains the same when its digits are reversed Composing literature in palindromes is an example of constrained writing. Constrained writing is a Literary technique in which the writer is bound by some condition that forbids certain things or imposes a pattern The word "palindrome" was coined from Greek roots palin (πάλιν; "back") and dromos (δρóμος; "way, direction") by English writer Ben Jonson in the 1600s. Benjamin Jonson ( c 11 June 1572 &ndash 6 August 1637) was an English Renaissance Dramatist The actual Greek phrase to describe the phenomenon is karkinikê epigrafê (καρκινική επιγραφή; crab inscription), or simply karkiniêoi (καρκινιήοι; crabs), alluding to the backward movement of crabs, like an inscription which can be read backwards. Crabs are decapod Crustaceans of the infraorder Brachyura, which typically have a very short projecting "tail" (βραχύ / brachy

History

Palindromes date back at least to 79 A. The Sator Square is a Word square containing a Latin Palindrome featuring the words SATOR AREPO TENET OPERA ROTAS written in a square D. , as the palindromic Latin word square "Sator Arepo Tenet Opera Rotas" was found as a graffito at Herculaneum, buried by ash in that year. The Sator Square is a Word square containing a Latin Palindrome featuring the words SATOR AREPO TENET OPERA ROTAS written in a square Herculaneum (in modern Italian Ercolano) is an ancient Roman town located in the territory of the current commune of Ercolano. This palindrome is remarkable for the fact that it also reproduces itself if one forms a word from the first letters, then the second letters and so forth. Hence it can be arranged into a word square that reads in four different ways: horizontally or vertically from top left to bottom right or horizontally or vertically from bottom right to top left. A word square is a special case of Acrostic. It consists of a set of words all having the same number of letters as the total number of words (the "order" of the square

While some sources translate this as "The sower Arepo holds the wheels at work", translation is problematic as the word arepo is otherwise unknown; the square may have been a coded Christian signifier, with TENET forming a cross. For further discussion, see separate article. The Sator Square is a Word square containing a Latin Palindrome featuring the words SATOR AREPO TENET OPERA ROTAS written in a square

A palindrome with the same property is the Hebrew palindrome "We explained the glutton who is in the honey was burned and incinerated" (פרשנו רעבתן שבדבש נתבער ונשרף; PRShW R`BTN ShBDBSh NTB`R WNShRP or parasnu ra`avtan sheba'dvash nitba'er venisraf) by Ibn Ezra, referring to the halachic question as to whether a fly landing in honey makes the honey treif. Abraham ben Meir ibn Ezra ( Hebrew: אברהם אבן עזרא or ראב"ע, also known as Abenezra) (1092 or 1093–1167 was one of the Halakha ( הלכה; alternative transliterations include Halocho and Halacha) is the collective body of Jewish Religious law Kashrut (also kashruth or kashrus, he כַּשְׁרוּת refers to Jewish dietary laws.

פ ר ש נ ו
ר ע ב ת ן
ש ב ד ב ש
נ ת ב ע ר
ו נ ש ר ף

Another Latin palindrome, "In girum imus nocte et consumimur igni" ("We enter the circle at night and are consumed by fire"), was said to describe the behavior of moths. It is likely from medieval rather than ancient times.

Byzantine Greeks often inscribed the palindrome "Wash the sins, not face alone" (Medieval Greek: ΝΙΨΟΝΑΝΟΜΗΜΑΤΑΜΗΜΟΝΑΝΟΨΙΝ; Modern: Νίψον ανομήματα μη μόναν όψιν; Nipson anomēmata mē monan opsin, note ps is the single Greek letter psi (Ψ)) on baptismal fonts. Medieval Greek (Μεσαιωνική Ελληνική is a linguistic term that describes the fourth period in the history of the Greek language. Modern Greek (el Νέα Ελληνικά or el Νεοελληνική lit A baptismal font is an article of church Furniture or a Fixture used for the Baptism of children and adults This is round the font at St. Mary's Church, Nottingham and also the font in the basilica of St. Sophia, Constantinople, the font of St. The Church of St Mary the Virgin is the oldest religious foundation in the City of Nottingham, England, and is also the largest church after the Roman Catholic Hagia Sophia (Ayasofya Αγία Σοφία " Holy Wisdom " Sancta Sophia or Sancta Sapientia) is a former patriarchal Basilica, later Constantinople (Κωνσταντινούπολις Konstantinoúpolis, or gr ἡ Πόλις hē Polis, Latin: la CONSTANTINOPOLIS Stephen d’Egres, Paris; at St. Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city Menin’s Abbey, Orléans; at Dulwich College; and at the following churches: Worlingsworth (Suffolk), Harlow (Essex), Knapton (Norfolk), St Martin, Ludgate (London), and Hadleigh (Suffolk). This article is about the French city of Orléans for other meanings see Orleans (disambiguation. Dulwich College is an independent selective fee-paying public school for boys in Dulwich, a suburb of south-east London United Kingdom Harlow is a New town and local government district in Essex, England. Knapton is a village and a Civil parish in the English county of Norfolk. St Martin Ludgate is a Church of England church on Ludgate Hill in the ward of Farringdon in the City of London. Hadleigh is an ancient Market town in Suffolk, East Anglia, England.

Types

Characters

The most familiar palindromes, in English at least, are character-by-character: the written characters read the same backwards as forwards. Palindromes may consist of a single word (civic, level, racecar, Malayalam), or a phrase or sentence ("Neil, a trap! Sid is part alien!", "Was it a rat I saw?", "Mr. Owl ate my metal worm", "Sit on a potato pan, Otis", "Satan, oscillate my metallic sonatas", "Rats live on no evil star. "). Spaces, punctuation and case are usually ignored. Much longer palindromic compositions have been constructed; see "Long palindromes", below.

Three famous English palindromes are "Able was I ere I saw Elba"^[1] (which is also palindromic with respect to spacing), "A man, a plan, a canal—Panama!”,^[2] and “Madam, in Eden I'm Adam,”. ^[3] The last example is still palindromic if "in Eden" is omitted; the response is either the one-word palindrome, "Eve," or the more obscure "Name no one man. "

Some individuals have names that are palindromes. Some changed their name in order to be a palindrome (one example is actor Robert Trebor), while others were given a palindromic name at birth (such as Neo-Nazi philologist Revilo Oliver). Robert Trebor (born June 7 1953) is an American character actor perhaps best known for his role as "Salmoneus" on the cult hits Hercules The This article is about the college professor For the Cartoonist, see ' Revilo ' Fictional names include Stanley Yelnats, the main protagonist in the book Holes by Louis Sachar. In the movie In the movie version Stanley is played by Shia LaBeouf. Holes is a Newbery Medal -winning Novel by Louis Sachar. It was later adapted into a screenplay for the 2003 film by Walt

Words

Some palindromes use words as units rather than letters. Examples are "fall leaves after leaves fall", "First Ladies rule the State and state the rule: ladies first" and "Girl, bathing on Bikini, eyeing boy, sees boy eyeing bikini on bathing girl". The command "Level, madam, level!", composed only of words that are themselves palindromes, is both a character-by-character and a word-by word palindrome.

Lines

Still other palindromes take the line as the unit. The poem Doppelganger, composed by James A. A doppelgänger ( or fetch is the ghostly double of a living person a sinister form of Bilocation. Lindon, is an example.

The dialogue "Crab Canon" in Douglas Hofstadter's Gödel, Escher, Bach is nearly a line-by-line palindrome. Douglas Richard Hofstadter (born February 15 1945 in New York New York) is an American academic whose research focuses on consciousness thinking and creativity Gödel Escher Bach an Eternal Golden Braid (commonly GEB) is a Pulitzer Prize -winning book by Douglas Hofstadter, described The second half of the dialog consists, with some very minor changes, of the same lines as the first half, but in reverse order and spoken by the opposite characters (i. e. , lines spoken by Achilles in the first half are spoken by the Tortoise in the second, and vice versa). In the middle is a non-symmetrical line spoken by the Crab, who enters and spouts some nonsense, apparently triggering the reversal. The structure is modeled after the musical form known as crab canon, in particular the canon a 2 cancrizans of Johann Sebastian Bach's The Musical Offering. A crab canon is an arrangement of two things that are complementary and backward similar to a Palindrome. WikipediaWikiProject Composers#Lead section.2 This article is written in British English including maximised use of "-ise" The Musical Offering (German title Musikalisches Opfer or Das Musikalische Opfer) BWV 1079 is a collection of canons

Numbers

Main article: Palindromic number

A palindromic number is a number where the digits, with decimal representation usually assumed, are the same read backwards, for example, 58285. A palindromic number or numeral palindrome is a 'symmetrical' number like 16461 that remains the same when its digits are reversed The decimal ( base ten or occasionally denary) Numeral system has ten as its base. They are studied in recreational mathematics where palindromic numbers with special properties are sought. Recreational mathematics is an umbrella term referring to Mathematical puzzles and Mathematical games. A palindromic prime is a palindromic number that is a prime number. A palindromic prime (sometimes called a palprime) is a Prime number that is also a Palindromic number. In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1

Dates

Palindromic dates are of interest to recreational mathematicians and numerologists, and sometimes generate comment in the general media. Numerology is any of many Systems Traditions or Beliefs in a mystical or Esoteric relationship between Numbers and physical ^[4] Whether or not a date is palindromic depends on the style in which it is written. For example, in the dd/mm/yyyy style, the 20th February 2002 (20-02-2002) was palindromic.

Music

Joseph Haydn's Symphony No. 47 in G is nicknamed the Palindrome. The third movement, minuet and trio is a musical palindrome. A minuet, sometimes spelled menuet, is a Social dance of French origin for two persons usually in 3/4 time. This clever piece goes forward twice and backwards twice and arrives back at the same place.

The interlude from Alban Berg's 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. Alban Maria Johannes Berg (February 9 1885 &ndash December 24 1935 was an Austrian Composer. Lulu is an Opera by the Composer Alban Berg. The Libretto was adapted by Berg himself from Frank Wedekind 's plays In Music, arch form is a sectional structure for a piece of music based on Repetition, in reverse order of all or most musical sections such James Tenney ( August 10, 1934 - August 24, 2006) was an American Composer and influential music theorist. Béla Viktor János Bartók (March 25 1881&ndashSeptember 26 1945 was a Hungarian Composer and Pianist, considered to be one of the greatest George Crumb also used musical palindrome to text paint the Federico Garcia Lorca poem "¿Porque nací?", the first movement of three in his fourth book of Madrigals. George Crumb (born October 24, 1929) is an American Composer of modern and Avant garde music Federico García Lorca' ( 5 June 1898 &ndash 19 August 1936) was a Spanish Poet and dramatist also remembered as A madrigal is a type of Secular vocal music composition written during the Renaissance and early Baroque eras Igor Stravinsky's final composition, The Owl and the Pussy Cat, is a palindrome. Igor Fyodorovich Stravinsky (Игорь Фёдорович Стравинский) ( &ndash 6 April 1971 was a Russian born Composer, considered by many to British composer Robert Simpson also composed music in the palindrome or based on palindromic themes; the slow movement of his Symphony No. 2 is a palindrome, as is the slow movement of his String Quartet No. Robert (Wilfred Levick Simpson ( 2 March 1921 &ndash 21 November 1997) was an English Composer and long-serving BBC The Symphony No 2 by Robert Simpson was completed in 1956 and dedicated to Anthony Bernard, conductor of the London Chamber Orchestra, though the first 1.

The music of Anton Webern is often imbued with palindromes. WikipediaWikiProject Composers#Lead section --> Anton Webern (December 3 1883 &ndash September 15 1945 was an Austrian Composer Webern, who had studied the music of the Renaissance composer Heinrich Issac, was extremely interested in symmetries in music, be they horizontal or vertical. Heinrich Isaac (also known as Ysaac, Henricus, Arrigo d'Ugo, and Arrigo il Tedesco – Tedesco meaning "Flemish" or "German" For one of the most famous examples of horizontal or linear symmetry in Webern's music, one should look no further than the first phrase in the second movement of the Opus 21 Symphony. A symphony is a Musical composition, often extended and usually for Orchestra. In one of the most striking examples of vertical symmetry, the second movement of the Opus 27 Piano Variations, Webern arranges every pitch of this dodecaphonic work around the central pitch axis of A4. The Piano Variations of American Composer Aaron Copland were written for piano solo from January to October of 1930 Twelve-tone technique (also dodecaphony, especially in British usage twelve-note composition) is a method of musical composition devised by Arnold From this, each downward reaching interval is replicated exactly in the opposite direction. For example, a G-sharp3 – 13 half-steps down from A4 – is replicated as a B-flat5 – 13 half-steps above.

In classical music, a crab canon is a canon in which one line of the melody is reversed in time and pitch from the other. Classical music is a broad term that usually refers to mainstream music produced in or rooted in the traditions of Western liturgical and Secular music A crab canon is an arrangement of two things that are complementary and backward similar to a Palindrome. In Music, a canon is a contrapuntal composition that employs a Melody with one or more imitations of the melody played after a given duration (e

The song "The Divided Sky" by Phish, from the 1988 album Junta, contains a brief musical palindrome near the beginning of the song. Phish is an American Jam band noted for their Musical improvisation, extended Jam sessions and cult following

On the 1999 album Ágætis byrjun by Sigur Rós, the song "Starálfur" contains palindromic string arrangements. Ágætis byrjun ( Icelandic for "An alright start" is the second Album by the Icelandic Post-rock band Sigur Sigur Rós ( are an Icelandic Post-rock band with melodic classical and minimalist elements Their 2005 album Takk... also contains the palindromic songs "Hoppípolla" and "Með Blóðnasir. Takk ( Thanks) is the fourth full-length studio album by the Icelandic band Sigur Rós. "

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 intro of the former song played in reverse. For other uses see Husker Du. Hüsker Dü was an American Alternative rock band formed in Minneapolis-St Zen Arcade is the third Studio album from the American rock band Hüsker Dü, released in July 1984 on SST Records. In Music, the introduction is a passage or section which opens a movement or a separate piece. Similarly, The Stone Roses' first album contains the songs "Waterfall" and "Don't Stop," the latter of which is essentially the former performed backwards. The Stone Roses were an English Alternative rock band formed in Manchester in 1984 The Stone Roses is the debut album by English Indie rock band The Stone Roses, released on. Waterfall is the 9th single from The Stone Roses. It was the fourth single taken from their debut album The Stone Roses.

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. UFO Tofu was the third album released by Béla Fleck and the Flecktones, released in 1992 Béla Fleck and the Flecktones is a multi- Grammy winning primarily instrumental group from the USA, that draws equally on bluegrass, fusion

Lutenist/composer Jozef van Wissem has produced two CDs consisting of palindrome compositions for lute, electronics, and field recordings made in railway stations and airport lounges. They are entitled Objects in Mirror are Closer than They Appear (BVhaast 0905) and Stations of the Cross (Incunabulum 004).

On his 1999 CD Thrash, Canadian rock soloist Nash the Slash features a track entitled "Theory of the Black Hole". Nash the Slash is a Canadian Progressive rock, classical, and alternative musician The recording beings with a rhythm track recorded backwards with music and narration played forwards, the song then repeats itself reversed, with the rhythm track playing forwards and the music and narration played backwards.

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. Joseph Waters (1952- is a member of the first generation of American classical composers who grew up playing in rock bands Entitled Crab Carillon, the result is a set of 488 tuned chimes, that can 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. The music can be heard on the City of San Diego Public Art Website.

"Weird Al" Yankovic's song "Bob", from his 2003 album Poodle Hat, consists of rhyming palindromes and parodies the Bob Dylan song Subterranean Homesick Blues. Alfred Matthew "Weird Al" Yankovic (ˈjæŋkəvɪk born October 23 1959 is a Grammy Award winning American singer Musician, actor satirist " Bob " is a song and video by "Weird Al" Yankovic, from his 2003 album Poodle Hat, made up entirely of Palindromes The Poodle Hat is the eleventh Album by "Weird Al" Yankovic. Bob Dylan (born Robert Zimmerman, May 24 1941 in Duluth, Minnesota) is an American singer-songwriter author poet and painter who has been a major " Subterranean Homesick Blues " is a Song by Bob Dylan, originally released on the album Bringing It All Back Home in March 1965

The song "I Palindrome I", by They Might Be Giants, features palindromic lyrics and imagery. I Palindrome I is an EP from They Might Be Giants. The title song also appears on Apollo 18 (1992 released in 1992 by Elektra Records They Might Be Giants (commonly abbreviated to TMBG) is an American Alternative rock band which began as a duo of John Flansburgh and John The 27-word bridge is word-symmetrical.

The song Bleeding Brain Grow by MC Paul Barman has five palindromes in a row. MC Paul Barman is a white Jewish Rapper from Ridgewood New Jersey, who attended Brown University.

The 2007 re-release of Yoko Ono's song "No, No, No" is credited simply to "Ono", making the artist–title combination a palindrome. born in Tokyo on February 18 1933 is a Japanese Artist and Musician. " No No No " is a song by Yoko Ono from her controversial 1981 album Season of Glass.

Acoustic

A palindrome in which a recorded phrase of speech sounds the same when it is played backwards was discovered by 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. John Oswald (born May 30, 1953 in Kitchener Ontario) is a Canadian Composer, saxophonist media artist and dancer The cut-up technique, also known as fishbowling, is an Aleatory Literary technique or genre in which a text is cut up at Random William Seward Burroughs II ( – ˈbʌroʊz was an American Novelist, Essayist, Social critic, painter and Spoken word Oswald discovered in repeated instances of Burroughs speaking the phrase "I got" that the recordings still sound like "I got" when played backwards. ^[5][6]

Computer programs

Brian Westley wrote a C program for the 1987 International Obfuscated C Code Contest which is a line-by-line palindrome. tags please moot on the talk page first! --> In Computing, C is a general-purpose cross-platform block structured The International Obfuscated C Code Contest (abbreviated IOCCC) is a Programming contest for the most creatively obfuscated C Code ^[7]

Up to the type definitions, here is a compilable almost palindrome written in Caml:

type 'a elbatum = 'a ;;
type lol = bool ;;
type pop = int ;;
type b = { mutable lol : lol elbatum } ;;
type i = { mutable pop : pop elbatum } ;;

fun erongi lol pop n ->
pop. Objective Caml ( OCaml) is the main implementation of the Caml Programming language, created by Xavier Leroy, Jérôme Vouillon  lol <- let nuf =
erongi;fun erongi lol pop n -> pop. lol ; ignore
n in
erongi ; lol. pop <- n pop lol ignore nuf ; ignore
= fun tel -> lol. pop
<- n pop lol ignore nuf
;;

The problem lies in the angle brackets, which are reversed when reading backwards from the end.

Long palindromes

Single words

The longest palindromic word in the Oxford English Dictionary is the onomatopoeic tattarrattat, coined by James Joyce in Ulysses (1922) for a knock on the door. Onomatopoeia (also spelled onomatopœia, from Greek: ονοματοποιΐα is a Word or a grouping of words that imitates the sound it is describing James Augustine Aloysius Joyce (2 February 1882 &ndash 13 January 1941 was an Irish expatriate writer widely considered to be one of the most influential writers of the Ulysses is a novel by James Joyce, first serialized in parts in the American journal The Little Review from March 1918 to December 1920 The Guinness Book of Records gives detartrated, the past tense of detartrate, a somewhat contrived chemical term meaning to remove tartrates. A tartrate is a Salt or Ester of the Organic compound Tartaric acid, a Dicarboxylic acid. Rotavator, a trademarked name for an agricultural machine, is often listed in dictionaries. A rotary tiller, also known as a rototiller, rotavator, rotary hoe, power tiller, or rotary plough (in US plow is a motorised The term redivider (i. e. someone or something that redivides) is used by some writers but appears to be an invented term - only redivide and redivision appear in the "Shorter Oxford Dictionary". Malayalam, an Indian language, is of equal length. Not to be confused with the Malay language. Malayalam (മലയാളം malayāḷaṁ) is a Dravidian language used (Strictly, this name should be spelt either Malayaalam or Malayālam, as the next to last vowel is long. )

The Finnish word saippuakivikauppias (soap-stone vendor) is claimed to be the world's longest palindromic word in everyday use. Finnish ( or suomen kieli) is the language spoken by the majority of the population in Finland (92% As of 2006) and by ethnic Finns outside A meaningful derivative from it is saippuakalasalakauppias (soapfish bootlegger). An even longer effort is saippuakuppinippukauppias (soapdish batch seller) Koortsmeetsysteemstrook (fever measuring system strip) is probably the longest palindrome in Dutch, and Kuulilennuteetunneliluuk (bullet flightway tunnel hatch) is the longest palindrome in Estonian.

Palindromic texts

To celebrate the palindromic moment 20:02 02/20 2002, Peter Norvig wrote on that day (20 February 2002) a computer program which produced what may be the world's longest palindromic "sentence",^[8] running to 17,259 words. Peter Norvig is an American computer scientist. He is currently the Director of Research (formerly Director of Search Quality at Google Inc ^[9] The palindrome is an extension of Leigh Mercer's famous palindrome “A man, a plan, a canal—Panama!”,^[2] and is effectively just a random list of comma-separated nouns and acronyms, many of which are obscure. Norvig later surpassed his own record with a 17,826-word palindrome created 11 November 2007. ^[10] Norvig also mentions that Gerald M. Berns made a palindromic list of 31,358 words with 119,180 letters, not in the form of a sentence. ^[11] The palindrome was made in October 2007 with Berns' own rules which limit reuse of words and do not allow proper nouns. ^[12]

A palindrome of over 5000 words entitled A Gassy Obese Boy's Saga, composed by Will Thomas,^[13] forms a narrative that makes some, albeit rambling, sense.

In 1991, Gordon Dow composed a 306 word palindrome entitled Dog Sees Ada. ^[14]

The poet Graywyvern wrote a 427-line palindromic poem, The Angel of Death, in 2005. ^[15]

Two "palindromic novels" appeared, in limited editions, during the 1980s: Dr Awkward & Olson in Oslo by Lawrence Levine^[16] and Satire: Veritas by David Stephens. ^[17]

Demetri Martin, a stand-up comedian, wrote a poem titled "Dammit I'm Mad", which is a 223 word palindrome. Demetrios Evan Martin (born May 25 1973 in New York City, New York) is an Emmy Award -nominated and Perrier comedy award -winning American The poem does not use any made-up words and is grammatically correct. .

The "Grand Palindrome" (1969)^[18] by novelist Georges Perec is the longest palindrome published in French, with 5,566 letters. Georges Perec ( 7 March 1936 &ndash 3 March 1982) was a highly-regarded French

Infinite palindromes in Russian

The Russian language allows infinite palindromes. Russian ( transliteration:,) is the most geographically widespread language of Eurasia, the most widely spoken of the Slavic languages Here's a sample infinite palindromic dialog:

—Я дядя!

—А я тётя!

—А я дядя!

—А я тётя!

—А я дядя!

. . .

Transliteration (note that ya and yo are single letters in Russian):

—Ya dyadya!

—A ya tyotya!

—A ya dyadya!

—A ya tyotya!

—A ya dyadya!

. . .

Translation:

"I'm the uncle!"

"But I'm the aunt!"

"But I'm the uncle!"

"But I'm the aunt!"

"But I'm the uncle!"

. . .

Another infinite palindrome reads:

Коростели летели, летели, . . . , летели лет сорок (Korosteli leteli, leteli, . . . , leteli let sorok)

It means, "Landrails have been flying, flying, . . . , flying for forty years".

Biological structures

In most genomes or sets of genetic instructions, palindromic motifs are found. In classical genetics the genome of a Diploid Organism including Eukarya refers to a full set of chromosomes or genes in a Gamete, thereby History See also History of genetics The existence of genes was first suggested by Gregor Mendel (1822-1884 who in the 1860s studied inheritance However, the meaning of palindrome in the context of genetics is slightly different 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 backwards. Deoxyribonucleic acid ( DNA) is a Nucleic acid that contains the genetic instructions used in the development and functioning of all known Nucleotides are Organic compounds that consist of three joined structures a nitrogenous base a Sugar, and a Phosphate group Adenine is a Purine with a variety of roles in Biochemistry including Cellular respiration, in the form of both the energy-rich Adenosine Thymine is one of the four bases in the Nucleic acid of DNA that make up the letters ATGC Cytosine is one of the five main bases found in DNA and RNA. It is a Pyrimidine derivative with a Heterocyclic Aromatic ring Guanine is one of the five main Nucleobases found in the Nucleic acids DNA and RNA, the others being Adenine, Cytosine, For example, the sequence ACCTAGGT is palindromic because its complement is TGGATCCA, which is equal to the original sequence in reverse.

A palindromic DNA sequence can form a hairpin. Deoxyribonucleic acid ( DNA) is a Nucleic acid that contains the genetic instructions used in the development and functioning of all known Stem-loop intramolecular Base pairing is a pattern that can occur in single-stranded DNA or more commonly in RNA. Palindromic motifs are made by the order of the nucleotides that specify the complex chemicals (proteins) which, as a result of those genetic instructions, the cell is to produce. Nucleotides are Organic compounds that consist of three joined structures a nitrogenous base a Sugar, and a Phosphate group Proteins are large Organic compounds made of Amino acids arranged in a linear chain and joined together by Peptide bonds between the Carboxyl Genetics (from Ancient Greek grc-Latn genetikos, “genitive” and that from grc-Latn genesis, “origin” a discipline of Biology, is The cell is the structural and functional unit of all known living Organisms It is the smallest unit of an organism that is classified as living and is often called They have been specially researched in bacterial chromosomes and in the so-called Bacterial Interspersed Mosaic Elements (BIMEs) scattered over them. The Bacteria ( singular: bacterium) are a large group of unicellular Microorganisms Typically a few Micrometres in length bacteria have Recently a research genome sequencing project discovered that many of the bases on the Y chromosome are arranged as palindromes. The Y chromosome is the sex-determining Chromosome in most Mammals including Humans In mammals it contains the gene SRY, which triggers A palindrome structure allows the Y chromosome to repair itself by bending over at the middle if one side is damaged.

It is believed that palindromes are also found frequently in proteins,^[19][20] but their role in the protein function is not clearly known. It is recently ^[21] suggested that the prevalence existence of palindromes in peptides might be related to the prevalence of low-complexity regions in proteins, as there is a large chance to observe a palindrome in low-complexity sequences. Their prevalence might be also related to an alpha helical formation propensity of these sequences ^[21]. A common motif in the Secondary structure of Proteins the alpha helix (α-helix is a right-handed coiled conformation resembling a spring, in which

Computation theory

In the automata theory, a set of all palindromes in a given alphabet is a typical example of a language which is context-free, but not regular. An alphabet is a standardized set of letters basic written symbols each of which roughly represents a Phoneme, a Spoken language, either A formal language is a set of words, ie finite strings of letters, or symbols. In Formal language theory, a context-free language is a language generated by some Context-free grammar. This means that it is theoretically impossible for a computer with a finite amount of memory to reliably test for palindromes. (For practical purposes with modern computers, this limitation would only apply to incredibly long letter-sequences. )

Additionally, the set of palindromes cannot be reliably tested by a deterministic pushdown automaton, and is not LR(k) parseable. In Automata theory, a Pushdown automaton is a Finite automaton with an additional stack of symbols its transitions can take the top symbol on the stack In Computer science, an LR parser is a Parser for Context-free grammars that reads input from L eft to right and produces a '''R'''ightmost When reading a palindrome from left-to-right, It is essentially impossible to locate the “middle” until the entire word has been read.

Semordnilaps

Semordnilap is a name coined for a word or phrase that spells a different word or phrase backwards. "Semordnilap" is itself "palindromes" spelled backwards. Semordnilaps are also known as volvograms,^[22] heteropalindromes, semi-palindromes, half-palindromes, reversgrams, mynoretehs, reversible anagrams,^[23] word reversals, or anadromes. ^[24] They have also sometimes been called antigrams,^[24] though this term now usually refers to anagrams with opposing meanings.

These words are very useful in constructing palindromes; together, each pair forms a palindrome, and they can be added on either side of a shorter palindrome in order to extend it.

The longest single-word instances in English are probably of eight letters, of which examples are:

• stressed / desserts
• samaroid (resembling a samara) / dioramas

Other examples include:

• gateman / nametag
• deliver / reviled
• dennis / sinned
• straw / warts
• star / rats
• stop / pots
• lived / devil
• diaper / repaid
• smart / trams
• spit / tips
• live / evil
• dog / god

An emirp is a prime that becomes a different prime when the decimal digits are read backwards. A samara is a type of Fruit in which a flattened wing of fibrous papery tissue develops from the ovary wall The word diorama can refer either to a nineteenth century mobile theatre device or in modern usage a three-dimensional model usually enclosed in a glass showcase for a museum An emirp ( prime spelled backwards is a Prime number that results in a different prime when its Digits are reversed In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 The decimal ( base ten or occasionally denary) Numeral system has ten as its base.

Non-English palindromes

Palindromes in languages that use an alphabetic writing system work in essentially the same way as English palindromes. An alphabet is a standardized set of letters basic written symbols each of which roughly represents a Phoneme, a Spoken language, either A writing system is a type of Symbolic system used to represent elements or statements expressible in Language. In languages that use a writing system other than an alphabet (such as Chinese), a palindrome is still a sequence of characters from that writing system that remains the same when reversed, though the characters now represent words rather than letters.

The treatment of diacritics varies. A diacritic ( also called a diacritic or diacritical mark, point, or sign, is a small sign added to a letter to alter pronunciation In languages such as Czech and Spanish, letters with diacritics or accents (except tildes) are not given a separate place in the alphabet, and thus preserve the palindrome whether or not the repeated letter has an ornamentation. The tilde (~ (/ˈtɪldə/ is a Grapheme with several uses The name of the character comes from Spanish, from the Latin titulus However, in Swedish and other Nordic languages, A and A with a ring (å) are distinct letters and must be mirrored exactly to be considered a true palindrome. The North Germanic languages or Scandinavian languages make up one of the three branches of the Germanic languages, a sub-family of the Indo-European languages The letter A is the first letter in the Latin alphabet. Its name in English is a (eɪ plural A ring Diacritic may appear above or below letters It may be combined with some letters of the extended Latin alphabets in various contexts The letter Å represents various sounds in the Swedish, Finnish (although no native Finnish words contain the letter å Danish, Norwegian

Japanese

Japanese palindromes, called kaibun, rely on the hiragana syllabary. is a language spoken by over 130 million people in Japan and in Japanese emigrant communities Kaibun (回文 lit circle sentence is a Japanese equivalent of Palindrome, or in other words a sentence that read the same from the beginning to the end or from is a Japanese Syllabary, one component of the Japanese writing system, along with Katakana and Kanji; the Latin alphabet A syllabary is a set of written symbols that represent (or approximate Syllables which make up Words A symbol in a syllabary typically represents an optional An example is the word "newsprint" (しんぶんし, shi-n-bu-n-shi^?). The Japanese syllabary makes it possible to construct very long palindromes.

Chinese

A Chinese word is a character, and is not composed of letters or syllables. A Chinese character, also known as a Han character ( is a Logogram used in writing Chinese (hanzi Japanese ( Therefore, any Chinese word itself is a trivial palindrome. Chinese palindromes have to be phrases or sentences and are much more easy to construct than in languages written with an alphabet. Some examples of this are:

• "I love mother, mother loves me" (traditional Chinese: 我愛媽媽，媽媽愛我; simplified Chinese: 我爱妈妈，妈妈爱我; pinyin: Wǒ aì māmā, māmā aì wǒ)
• "Shanghai's tap water comes from the sea" (Chinese: 上海自來水來自海上; pinyin: Shànghǎi zì lái shuǐ lái zì hǎi shàng))
• "Sheung Shui residents live above the water" (traditional Chinese: 上水居民居水上; Cantonese Yale: seung5 seui2 geui1 man4 geui1 seui2 seung5). Pinyin, more formally Hanyu pinyin, is the most common Standard Mandarin Romanization system in use Shanghai ( 上[[wikt 海|海]] is the largest city in China in terms of population and one of the largest urban areas in the world with over 20 million Pinyin, more formally Hanyu pinyin, is the most common Standard Mandarin Romanization system in use Sheung Shui ( is part of the Fanling-Sheung Shui New Town in the North District of Hong Kong. The Yale romanizations are four systems created during World War II for use by United States military personnel.

Palindromic poetry (traditional Chinese: 回文詩; pinyin: huí wén shī) was a literary genre in classical Chinese literature. Pinyin, more formally Hanyu pinyin, is the most common Standard Mandarin Romanization system in use Classical Chinese or Literary Chinese is a traditional style of Written Chinese based on the Grammar and Vocabulary of ancient Chinese The "forward reading" and the "backward reading" of such a poem would be similar but not exactly the same in meaning. Although called "palindromic", these poems are often not palindromes in the normal English sense of the word. They do not necessarily have symmetry of characters or sound, but merely need to make sense when read in either direction (and would probably be better referred to as Semordnilaps). A palindrome is a word phrase number or other sequence of units that can be read the same way in either direction (the adjustment of punctuation and spaces between words The following example was composed during the Song Dynasty:

枯眼望遙山隔水，往來曾見幾心知。壺空怕酌一杯酒，筆下難成和韻詩。迷路阻人離別久，訊音無雁寄回遲。孤燈夜守長寥寂，夫憶妻兮父憶兒。

The "forward reading" of the last sentence is about husband missing wife and father missing son, while the "backward reading" is about son missing father and wife missing husband. The Song Dynasty ( Wade-Giles: Sung Ch'ao was a ruling dynasty in China between 960&ndash1279 CE it succeeded the Five Dynasties and Ten Kingdoms

Other languages

Some examples in other languages are:

• Amharic: "Tkus bskut" (Fresh cookie/biscuit. Amharic (አማርኛ amarəñña) is a Semitic language spoken in North Central Ethiopia by the Amhara. ) (Amharic is written with a syllabary, so the spelling of the palindrome is by syllables. A syllabary is a set of written symbols that represent (or approximate Syllables which make up Words A symbol in a syllabary typically represents an optional The "ku" of each word will be written by a single character, so it is spelled as a palindrome, similarly to the Japanese example above, also written with a syllabary. )
• Bengali:"রমাকান্ত কামার " (Romakanto Kamar) and "সুবল লাল বসু" (Subol Lal Bosu) - two names.
• Brazilian Portuguese: "Socorram-me, subi no onibus em Marrocos" (Help me, I took a bus in Morocco). Brazilian Portuguese ( Language code pt-BR Portuguese: português brasileiro or português do Brasil) is a group of Portuguese Morocco (المغرب "al-Maghrib" officially the Kingdom of Morocco (المملكة المغربية is a country located in North Africa "Ávido? Amá-la na taba, no toco da casa, no muro no paço, na poça, na maca, na livre sala, servi-la na cama, na copa, no capô, no rumo, na saca do coto, na bata, na lama. . . Ó diva!" (Hasty? Love her on the board, on the stub of the house, on the wall of the court, on the pool, on the hammock, free in the room, serve her on the bed, on the pantry, on the hood, on the stump, on the bathrobe, on the mud. . . oh diva!)
• Bulgarian: Az obicham mach i boza (Аз обичам мач и боза; "I like football and a drink", note ch is the single Bulgarian letter che (Ч)), Nasila zakaraha svinete ni v sahara! - kaza Lisan (Насила закараха свинете ни в Сахара! - каза Лисан; "They took our pigs to Sahara - said Lisan"). Bulgarian (български език IPA: ɛzˈik is an Indo-European language, a member of the Slavic linguistic group Che or Cha (Ч ч italics Ч ч) is a letter of the Cyrillic alphabet.
• Czech: "Kobyla má malý bok" (A mare has a low hip), "Jelenovi pivo nelej" (Do not pour beer for a stag). Czech (ˈʧɛk čeština ˈʧɛʃcɪna in Czech is a West Slavic language with about 12 million native speakers it is the majority language in the
• Danish: "Tre negre med fane, en af dem er genert" (Three negroes with (a) flag, one of them is shy). Danish ( d̥ænsɡ̊ is one of the North Germanic languages (also called Scandinavian languages a sub-group of the Germanic branch of the
• German: "Ein Neger mit Gazelle zagt im Regen nie” (A negro with a gazelle never quails in the rain). The German language (de ''Deutsch'') is a West Germanic language and one of the world's major languages.
• Dutch: "Nelli plaatst op 'n parterretrap 'n pot staalpillen" (Nelli places a jar of iron pills on the downfloor stairs)
• Esperanto: "Ora trovo: vortaro" (A golden find: a dictionary). Dutch ( is a West Germanic language spoken by around 24 million people 22 million of which are from the Netherlands, Belgium and Suriname Anemia ( AmE) or anæmia/anaemia ( BrE) (from the Ancient Greek grc-Latn anaîmia, meaning “without blood” is defined as a qualitative is by far the most widely spoken constructed International auxiliary language in the world
• Estonian: "Kuulilennuteetunneliluuk" (The hatch of the tunnel of ballistic trajectory), "Aias sadas saia" (It was raining white bread in the garden)
• Persian: "شو همره بلبل بلب هر مهوش ، شکر بترازوی وزارت برکش"
• Finnish: "Innostunut sonni" (an excited bull), "Saippuakivikauppias" (a lye salesman). Estonian (; ˈeːsti ˈkeːl is the official language of Estonia, spoken by about 1 Finnish ( or suomen kieli) is the language spoken by the majority of the population in Finland (92% As of 2006) and by ethnic Finns outside The latter is also the longest palindromic word in the world with a real meaning.
• French: "Esope reste ici et se repose" (Aesope stays there and rests), "Elu par cette crapule" (elected by this scoundrel). French ( français,) is a Romance language spoken around the world by 118 million people as a native language and by about 180 to 260 million people
• Greek: "Νίψον ανομήματα, μη μόναν όψιν" (Wash the sins, not only the face)
• Hebrew: "?אבי אל חי שמך למה מלך משיח לא יבא" (Eternal Father be Thy name, why hast the King Messiah not yet come?), "דעו מאביכם כי לא בוש אבוש, שוב אשוב אליכם כי בא מועד" (Know from your forefathers that I will not be embarrassed, I will return to you at the appointed time. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly )
• Hungarian: "Kis erek mentén, láp sík ölén odavan a bánya rabja: jaj, Baranyában a vadon élő Kis Pálnét nem keresik!" (Along the small streams and in the flat lap of the moorland gone the prisoner of the mine: oh, nobody looks for Ms. Hungarian ( magyar nyelv) is a Uralic language (more specifically a Ugric language) unrelated to most other languages in Europe. Kis Pál who lived in the woods of Baranya. )
• Irish: "A Nóinín, níl an rí anocht ar Ráth Conair, ná linn. Irish (ga ''Gaeilge'' is a Goidelic language of the Indo-European language family originating in Ireland and historically spoken by the Irish. In Iona. " ("Nettle, the king is neither tonight on Conair's fort, nor with us. In Iona. Iona is a small island in the Inner Hebrides of Scotland that has an important place in the history of Christianity in Scotland and is renowned for its tranquility ")
• Italian: "Autore, ero tua" (Author, I was yours), "I topi non avevano nipoti" (The mice had no grandchildren). Italian ( or lingua italiana) is a Romance language spoken by about 63 million people as a First language, primarily in Italy.
• Korean: "일요일" (Sunday), "스위스" (Switzerland), "사진사" (Photographer), "시흥시" (Siheung City), "소주 만병만 주소" (Please give me 10,000 bottles of alcohol), "다시 합창합시다" (Let's sing together again). This article is mainly about the spoken Korean language See Hangul for details on the native Korean writing system

  See also: Rokuko

• Latin: "Sum summus mus" (I am the greatest mouse), "Si nummi immunis" (If you have money, you will be free {an inscription on the door in a lawyer's office}), "In girum imus nocte et consumimir igni" (We enter the circle at night and are consumed by fire. "Rokkugo" ( Korean: 로꾸거!!! is the first CD single by Super Junior-T, released on February 23, 2007. Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. ")
• Latvian: "Alus ari ira sula" (Beer is juice too). Latvian language (latviešu valoda is the official state language of Latvia.
• Lithuanian: "Sėdėk užu kėdės" (Sit behind the chair). Lithuanian ( lietuvių kalba) is the official state language of Lithuania and is recognised as one of the official languages of the European Union.
• Norwegian: "Agnes i senga" (Agnes in bed). Norwegian ( norsk) is a North Germanic Language spoken primarily in Norway, where it is an official language
• Polish: "Może jutro ta dama da tortu jeżom" (Perhaps tomorrow this lady will give hedgehogs a cake). Polish ( język polski, polszczyzna) is the Official language of Poland.
• Romanian: "Aerisirea" (the ventilation); "Era o tipă răpitoare" (she was a ravishing woman); "Alina m-a luat să stau la Manila" (Alina took me to stay in Manila); a palindromic letter: "Dragă Ileana, aci m-a atacat Rada cu Luca, dar tac. Romanian or Daco-Romanian ( dated: Rumanian or Roumanian; self designation limba română, ˈlimba roˈmɨnə is a Romance A ta amică, Ana-Elia Gard" (Dear Ileana, here I was attacked by Rada and Luca, but I say nothing. Your friend, Ana-Elia Gard). ^[25] As usual in Romanian crosswords, scrabble, and other word games, diacritics in palindromes are often ignored.
• Russian: "Он дивен, палиндром: и ни морд, ни лап не видно" (On diven, palindrom: i ni mord, ni lap ne vidno; It's wonderful, a palindrome: and neither muzzles, nor paws are visible). Russian ( transliteration:,) is the most geographically widespread language of Eurasia, the most widely spoken of the Slavic languages
• Serbian: "Ana voli Milovana" (Ana loves Milovan)
• Slovenian: "Perica reže raci rep" (Washing woman is cutting the duck's tail); "Ona seksa skesano" (She's having sex with remorse)
• Spanish: "Dábale arroz a la zorra el abad" (The abbott was giving rice to the vixen), "La ruta nos aportó otro paso natural" (The route provided us with another natural passage), "Anita lava la tina" (Anita cleans the bathtub). Serbian (sr-Cyrl српски језик sr-Latn ''srpski jezik'' is a South Slavic language, Slovene or Slovenian ( slovenski jezik or slovenščina, not to be confused with Slovenčina) is a South Slavic language
• Swedish: "Gnupung" (Gnu scrotum), "Ni talar bra Latin" (You speak Latin well), "Bor edra gråvita fat i vår garderob?" (Do your grey-white plates live in our wardrobe?). Swedish ( is a North Germanic language spoken by more than nine million people predominantly in Sweden and parts of Finland, especially along the
• Tagalog: "Nasa bayabasan" (In the guava fields). Tagalog is one of the major languages used in the Philippines.
• Tatar: "Ata kadak ata" (Father throws a nail). The Tatar language (,, Татар теле, Татарча) is a Turkic Language spoken by the Tatars.
• Telugu: "vikatakavi" (comedy poet).
• Turkish: "Anastas kazak satsana" (Anastas, sell a sweater). Turkish ( tr Türkçe IPA) is a language spoken by over 63 million people worldwide making it the most commonly spoken of the Turkic languages.
• Welsh: "Lladd dafad ddall" (Kill a blind sheep), and "Nawr ydy rwan" (now [southern spelling] is now [northern spelling]). Welsh ( cy Cymraeg or cy y Gymraeg, kəmˈrɑːɨɡ and {{IPA|[ə ɡəmˈrɑːɨɡ]}}, is a member of the Brythonic branch of Celtic
• Tamil (when written in Tamil script): "Maama" (maternal uncle)(மாமா), "Paappa" (a girl child) (பாப்பா), "Kakka" (crow) (காக்கா), "Kee Kee" (sound of parrot) (கீக்கீ), "Thaatha" (Grandpa) (தாத்தா), "Thelu Meeluthey" (scorpion returns) (தேளு மீளுதே), "Vi-ka-ta-ka-vi" (விகடகவி). Tamil (ta தமிழ்; t̪əmɨɻ is a Dravidian language spoken predominantly by Tamil people of the Indian subcontinent. The

See also

• Ambigram
• Anagram
• Backmasking
• List of palindromic places
• Phonetic palindrome
• Palindromic number
• Palindromic polynomial
• Reverse spelling

References

External links

• Daft Fad, Computer Generated Palindromes
• International Palindromes
• Palindrome of the Day
• The best palindrome

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