What is a palindrome? Palindromes are examples. English palindromes

As is known, the Russian language is quite voluminous in terms of the variety of phrases and expressions. One of the varieties of lexical elements are palindromes. Examples for children, most accurately illustrating this concept, you can search the classics. For example, Fet: "A rose fell on the paw of Azora." If you look closely at the words, you can see that the sentence can be read in both directions: from the beginning (from left to right) and from the end (from right to left). And in each case the expression will sound the same. These are suggestions, but there are also palindrome words. Examples that most clearly illustrate the concept will be given below.

Definition

What is a palindrome? This concept has Greek roots and is literally translated as "running back" or "running again". In some cases, for palindromes, examples of which will be given below, take any symmetric in relation to their own mid-range of characters. The longest combination of this type is saippuakauppias (from Finnish - the seller of soap). There are quite interesting English palindromes:

"Madam, I'm Adam" is a representation of a man to a lady (Madame, I am Adam).

At this lady can modestly answer "flip-flop": "Eve" (Eva).

There are symmetrical not only sentences or sets of letters. Palindrome-verses are quite common:

I rarely hold my butt with my hand ...
I'm already sitting here,
Yaro in the quiet, creating,
Zarzhu just once
Luck in the chad,
Already I am getting rusty -
Yes, I'm glad!

You can read both from the beginning and from the end.

A Brief Historical Reference

Speaking of what a palindrome is, one should say that there are "changers" from the deepest antiquity. Often they were given a magical sacral meaning. There were palindromes, examples of which can be found in a variety of languages, presumably in the Middle Ages. In classical Russian literature there is reliable information about the author's "flip-flop" written by Derzhavin: "I am going with a sword judge". The first attempt to compose a long, multi-line rhymed product of the palindrome type was undertaken by Velimir Khlebnikov (the poem "Razin"). But this artistic direction flourished only in the 1970s and 1990s. Palindromes, examples of which can be found in the works of Vladimir Gershuni, Nikolay Ladygin, Dmitry Avalini and Elena Katsyuba, began to be studied in more detail in literary and literary directions in the 1990s. Research was actively conducted, mainly by Herman Lukomnikov and Alexander Bubnov. Theorists and practitioners distinguished various boundary forms. For example, "werewolf". This text is read from left to right differently than back: "The world is convenient" (author Sergei Fedin). Speaking of what a palindrome is, one should also mention the rare forms of this artistic direction: these are syllabic, bilingual "flips". The latter are text that can be read in one language in one language, and vice versa on the other. What other rare palindromes are there? Examples can be given different. There is a form of "symmetric" combination, in which reading is not in reverse, but in a multiplicated form: tsokoltsokol, kabankaban and others.

Interest in the direction

It should be said that palindromes, examples of which will be given further in the article for greater clarity, were of interest to researchers of vocabulary, writers, poets, writers at different times to varying degrees. It is noteworthy that in the seventies of the last century it was impossible to publish such works. This was mainly due to the fact that the desire for "formalism" at the time was not welcomed in the literature. At the very beginning of the development of this artistic direction, all the writers of the "flip-flops" were well acquainted with each other, they knew, one can say, in the face of each other. To date, many works have been published in anthologies. But most of them remained unpublished.

Genres

Palindromes-phrases, or "aphorisms" were very popular. Some of them could even cause a smile (due to their artistic features). In many cases, the combination inside the flip-flop attracted attention not only with its non-standard form, but also with a certain humorous content. Individual lines can even be collected in a poetic work. However, if the combinations pretend to poetry after all, then they should not allow any discounts on the unusual forms. In other words, everything should be preserved - rhythm, rhyme, dimensions - as in standard, ordinary verse works. "Symmetry" in such cases added only a rhythmic and sound game. Many poets could find "almost palindromic" forms. At different authors such turns created beauty of sounding. Speaking of what a palindrome is, one can not help but consider the lyrical poetic works created with the use of these art forms. Many of them contain a share of humor, but, despite this, can be taken seriously enough. Some symmetrical expressions fit well into music. In a number of cases a poetic work can consist of one "flip-flop", divided into strings. In this case, they speak of a mono-palindrome.

Poetry

Blok's creativity is of special interest against the backdrop of research on palindromes . Being a poet-symbolist, he paid a lot of attention to the rhythmic and sound organization of works. His poem "The Twelve" clearly traces the achievements of Alexander Blok in the sound and rhythmic directions. Goldstein translated all this work of Blok into the language of palindromes. At the same time the author notes that in the process it was possible to preserve rhyme, rhythm, composition of the entire poem almost everywhere. Redesigned "Twelve", Goldstein notes that, in his opinion, some shifted accents even to a certain extent enhance intonation.

Symmetry in figures

There are, except for letters, expressions and whole works and palindrome numbers. This definition is used with the apparent symmetry in the record. Natural numbers in this case will be read from left to right and vice versa alike. Symmetrically can be arranged as an odd or even number of characters. Numerical palindromes occur in different systems that have their own names. So, there is a category of "figured" signs: 1001, 676 and others. Such "palindromic" forms are found among Fibonacci numbers, Smith numbers .

Mathematical Actions

Numerical palindromes can be the result of operations on other signs. Martin Gardner, the author of the book "There is an idea!", Being a well-known popularizer of science, puts forward a certain hypothesis. If we take a natural number (any) and add an inverted (consisting of the same digits, but in the reverse order), then repeat the action, but with the resulting sum, then one of the steps will turn out to be a palindrome. In some cases it is sufficient to perform the addition once: 213 + 312 = 525. But usually not less than two operations are necessary. So, for example, if you take the number 96, then, after making a sequential addition, you can get the palindrome only on the fourth level:

96 + 69 = 165
165 + 651 = 726
726 + 627 = 1353
1353 + 3531 = 4884

The essence of the hypothesis is that if you take any number, after a certain number of actions will necessarily be received by a palindrome. Examples can be found not only in addition, but also in the construction of a degree, extraction of roots and other operations.

Interesting pairs

In groups of prime numbers, one can observe very interesting regularities, if there are specific numbers, say, simple ones - 1 and 3. Thus, simple two-valued will be ordered pairs: 31-13 and 13-31, out of six three-figure simple will be five, among which 2 "Werewolf": 313 and 131, pairs of shifters: 113-311 and 311-113. The pairs obtained in all presented cases are clearly expressed in the form of numerical squares. In general, in mathematics you can find a lot of digital patterns.

Palindromes in other spheres of human activity. Biology

The structure of nucleic acids provides for the presence of relatively short mutually complementary regions. They have so-called "mirror sequences" of nucleotides, capable of forming duplexes. In the human genome, the total number of such "flips" is estimated to range from one hundred thousand to one million. In this case, according to observations, their distribution over the DNA structure is uneven. Palindromes in the biological sense have the ability to provide an increase in the amount of information without increasing the number of nucleotides. Of particular importance are "symmetrical forms" when certain types of nucleic acids are formed-transport RNA, for example.

Music

Palyndromic music is played "as usual", in accordance with the rules. After the song is over, the notes are flipped over. Then the work is played again, but the melody will not change at the same time. Iterations can be present as many as you like, it is not known at the same time what is the bottom and what is on horseback. These musical works can be played together, while reading notes from both sides simultaneously. Examples of such palindrome works are "The Way of the World" written by Mosheles, and "The Tablet Melody for Two", composed by Mozart.