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A palindrome is a word, number , phrase, or other sequence of characters which reads the same backward as forward, such as madam or racecar. For example; Tuesday, 22 February is considered a palindrome day using dd-mm-yyyy format as it can be read from left to right or vice versa.

The word palindrome was introduced by Henry Peacham in The ancient Greek poet Sotades 3rd century BCE invented a form of Ionic meter called Sotadic or Sotadean verse, which is sometimes said to have been palindromic, [4] but no examples survive, [5] and the exact nature of the “reverse” readings is unclear.

A palindrome was found as a graffito at Herculaneum , a city buried by ash in 79 CE. 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. The palindromic Latin riddle ” In girum imus nocte et consumimur igni ” “we go in a circle at night and are consumed by fire” describes the behavior of moths.

It is likely that this palindrome is from medieval rather than ancient times. The second word, borrowed from Greek, should properly be spelled gyrum. This is generally considered to be the first English-language palindrome sentence, and was long reputed notably by the grammarian James “Hermes” Harris to be the only one, despite many efforts to find others.

In recent history, there have been competitions related to palindromes, such as the World Palindrome Championship, set in Brooklyn, USA. The most familiar palindromes in English are character-unit palindromes. The characters read the same backward as forward. Some examples of palindromic words are redivider , deified , civic , radar , level , rotor , kayak , reviver , racecar , madam , and refer. There are also word-unit palindromes in which the unit of reversal is the word “Is it crazy how saying sentences backwards creates backwards sentences saying how crazy it is?

Word-unit palindromes were made popular in the recreational linguistics community by J. Lindon in the s. Occasional examples in English were created in the 19th century.

Several in French and Latin date to the Middle Ages. There are also line-unit palindromes, most often poems. These possess an initial set of lines which, precisely halfway through, is repeated in reverse order, without alteration to word order within each line, and in a way that the second half continues the “story” related in the first half in a way that makes sense, this last being key. Palindromes often consist of a sentence or phrase, e. Owl ate my metal worm”, “Do geese see God?

Punctuation, capitalization, and spaces are usually ignored. Some, such as “Rats live on no evil star”, “Live on time, emit no evil”, and “Step on no pets”, include the spaces. Lon Nol — was Prime Minister of Cambodia. Some people have changed their name in order to make it palindromic such as actor Robert Trebor and rock-vocalist Ola Salo , while others were given a palindromic name at birth such as the philologist Revilo P.

There are also palindromic names in fictional media. The s pop band ABBA is a palindrome using the starting letter of the first name of each of the four band members.

The digits of a palindromic number are the same read backwards as forwards, for example, ; decimal representation is usually assumed. In recreational mathematics , palindromic numbers with special properties are sought. For example, and are palindromic primes. Whether Lychrel numbers exist is an unsolved problem in mathematics about whether all numbers become palindromes when they are continuously reversed and added. Numbers such as are thought to never become palindromes when this reversal process is carried out and are therefore suspected of being Lychrel numbers.

If a number is not a Lychrel number, it is called a “delayed palindrome” 56 has a delay of 1 and 59 has a delay of 3. Several smaller delay palindromes were published separately as A Every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater. A day or timestamp is a palindrome when its digits are the same when reversed.

Only the digits are considered in this determination and the component separators hyphens, slashes, and dots are ignored. A notable palindrome day is this century’s 2 February because this date is a palindrome regardless of the date format by country yyyy-mm-dd, dd-mm-yyyy, or mm-dd-yyyy used in various countries.

For this reason, this date has also been termed as a “Universal Palindrome Day”. A phonetic palindrome is a portion of speech that is identical or roughly identical when reversed. It can arise in context where language is played with, for example in slang dialects like verlan. Talk, Roy”, and “You’re damn mad, Roy”.

Joseph Haydn ‘s Symphony No. In the third movement, a minuet and trio , the second half of the minuet is the same as the first but backwards, the second half of the ensuing trio similarly reflects the first half, and then the minuet is repeated.

Lambert claimed that the theme was dictated to him by the ghost of Bernard van Dieren , who had died in British composer Robert Simpson also composed music in the palindrome or based on palindromic themes; the slow movement of his Symphony No. His hour-long String Quartet No. All of Simpson’s thirty-two variations are themselves palindromic. It is essentially a dramatic palindrome.

Through the first half, a tragedy unfolds between two lovers, involving jealousy, murder and suicide. Then, in the reversing second half, this is replayed with the lines sung in reverse order to produce a happy ending.

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. A striking example of vertical symmetry is the second movement of the Piano Variations , Op. From this, each downward reaching interval is replicated exactly in the opposite direction.

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 , consists of twenty sections, called “moments”, which may be 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 , 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. It is a perfect example of Goeyvaerts’s aesthetics, the perfect example of the imperfection of perfection. 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.

This is usually a form of reference to the crucifixion; for example, the 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 centre of the cross in the crucifixion.

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.

The longest palindromic word in the Oxford English Dictionary is the onomatopoeic tattarrattat , coined by James Joyce in Ulysses for a knock on the door. 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 , a language of southern India, is of equal length. English palindromes of notable length include mathematician Peter Hilton ‘s “Doc, note: I dissent.

A fast never prevents a fatness. I diet on cod” [42] and Scottish poet Alastair Reid ‘s “T. Eliot, top bard, notes putrid tang emanating, is sad; I’d assign it a name: gnat dirt upset on drab pot toilet. According to Guinness World Records , the Finnish letter word saippuakivikauppias a soapstone vendor , is the world’s longest palindromic word in everyday use. In most genomes or sets of genetic 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.

A palindromic DNA sequence may form a hairpin. Palindromic motifs are made by the order of the nucleotides that specify the complex chemicals proteins that, as a result of those genetic instructions, the cell is to produce. Recently [ when? It is believed that palindromes frequently are also found in proteins, [46] [47] but their role in the protein function is not clearly known.

It has recently [48] 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. In automata theory , a set of all palindromes in a given alphabet is a typical example of a language that is context-free , but not regular.

This means that it is impossible for a computer with a finite amount of memory to reliably test for palindromes. For practical purposes with modern computers, this limitation would apply only to impractically long letter-sequences. In addition, the set of palindromes may not be reliably tested by a deterministic pushdown automaton which also means that they are not LR k -parsable or 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.

It is possible to find the longest palindromic substring of a given input string in linear time. A palstar is a concatenation of palindromic strings, excluding the trivial one-letter palindromes — otherwise all strings would be palstars.

From Wikipedia, the free encyclopedia. Phrases that read the same backwards. For the film, see Palindromes film. Main article: Palindromic number. Main article: Periodic continued fraction.

 
 

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This glossary of climbing terms is a list of definitions of terms and jargon related to rock climbing and mountaineering.

Also V-thread. Also rappelling. Also schrund. Also bivy or bivvy. Also bomber. Also open book. Also chockstone. Also nut key or nut tool. Also decking. Also crimper.

Also cutting feet. Also rappel device. Also dex. Also half ropes. Also rope drag. Also drilled pitons. Also drop knee. Also Klettersteig. Also figure-eight loop. Also finger lock. Also heel-to-toe jam. Also free soloing. Also French climbing or French freeing. Also indoor climbing.

Also heel-toe cam. Also a hex. Also high ball. Also simply jug. Also kneebar. Also kneepad. Also liebacking. Also mantle. Also Italian hitch or friction hitch. Also nut tool. Also onsight. Also pinchers. Also Whittaker wheeze.

Also bouldering problem or boulder problem. Also mock leading. Also quickies , draws , and extenders. Also maillon and maillon rapide. Also abseil or roping down. Also roped team or roped party. Also rose move. Also read. Also Sirdar. Also foot chip , chip , or micro. Also scissor leg , Elvis Presley syndrome , or disco knee. Also simulclimbing. Also sit down start. Also soft loops.

Also trad climbing or simply trad. Also trolleying. Also undercut. Also Abalakov thread. Also jug up. Also Z-system. From Wikipedia, the free encyclopedia. List of definitions of terms and concepts related to rock climbing and mountaineering. For the Kanye West song, see On Sight. Golden age of alpinism History of rock climbing. Abseiling Belaying Grades.

Rock Climbing. Retrieved ISBN UK Climbing. Retrieved 29 April Retrieved 20 May Retrieved 20 May — via DocPlayer. Retrieved 13 March Sierra Mountain Guides. Retrieved March 23, Retrieved 8 December Retrieved July 4, Take the Test! Retrieved 12 December Retrieved 15 December How to Rock Climb! Tales from the rampage. What is a dab in climbing. Archived from the original on OCLC The DeadPoint”.

Climbing Tech Tips. A Handbook for Medical Officers”. US Army Research Inst. Irish Mountaineering Club. Steph Davis — High Places. Retrieved 9 December Do Not Do This! Mountain Project. Taylor Trade Publishing. The Food Timeline. Retrieved 20 December Send Climbing. Retrieved 1 January Stackpole Books. British Mountaineering Council.