5 (number)

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5 (number)
This article discusses the number five. For the year 5 AD, see 5. For other uses of 5, see 5 (disambiguation).
5
Cardinal 5
five
Ordinal 5th
fifth
Numeral system quinary
Factorization prime
Divisors 1, 5
Roman numeral V
Roman numeral (Unicode) Ⅴ, ⅴ
Greek ε (or Ε)
Arabic ٥,5
Arabic (Persian, Urdu) ۵
Ge'ez
Bengali
Punjabi
Chinese numeral 五，伍
Devanāgarī
Hebrew ה (Hey)
Khmer
Telugu
Malayalam
Tamil
Thai
prefixes penta-/pent- (from Greek)

quinque-/quinqu-/quint- (from Latin)

Binary 101
Octal 5
Duodecimal 5
Vigesimal 5 (5)

5 (five /ˈfv/) is a number, numeral, and glyph. It is the natural number following 4 and preceding 6.

In mathematics

Five is the third prime number. Because it can be written as 221+1, five is classified as a Fermat prime. 5 is the third Sophie Germain prime, the first safe prime, the third Catalan number, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. Five is the first good prime. It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. It is also the only number that is part of more than one pair of twin primes. Five is a congruent number. Five is conjectured to be the only odd untouchable number and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree.

The number 5 is the 5th Fibonacci number, being 2 plus 3. 5 is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), ... ( lists Markov numbers that appear in solutions where one of the other two terms is 5). Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers.

In bases 10 and 20, 5 is a 1-automorphic number.

5 and 6 form a Ruth–Aaron pair under either definition. The classification however may be frowned upon.

There are five solutions to Znám's problem of length 6.

Five is the second Sierpinski number of the first kind, and can be written as S2=(22)+1

While polynomial equations of degree 4 and below can be solved with radicals, equations of degree 5 and higher cannot generally be so solved. This is the Abel–Ruffini theorem. This is related to the fact that the symmetric group Sn is a solvable group for n ≤ 4 and not solvable for n ≥ 5.

While all graphs with 4 or fewer vertices are planar, there exists a graph with 5 vertices which is not planar: K5, the complete graph with 5 vertices.

Five is also the number of Platonic solids.[1]

A polygon with five sides is a pentagon. Figurate numbers representing pentagons (including five) are called pentagonal numbers. Five is also a square pyramidal number.

Five is the only prime number to end in the digit 5, because all other numbers written with a 5 in the ones-place under the decimal system are multiples of five. As a consequence of this, 5 is in base 10 a 1-automorphic number.

Vulgar fractions with 5 or 2 in the denominator do not yield infinite decimal expansions unlike expansions with most prime denominators, because they are prime factors of ten, the base. When written in the decimal system, all multiples of 5 will end in either 5 or 0.

There are five Exceptional Lie groups.

Evolution of the glyph

The evolution of our modern glyph for five cannot be neatly traced back to the Brahmin Indians quite the same way it can for 1 to 4. Later on the Indian Empires of Kushana and Gupta from India had among themselves several different glyphs which bear no resemblance to the modern glyph. The Nagari and Punjabi took these glyphs and all came up with glyphs that are similar to a lowercase "h" rotated 180°. The Ghubar Arabs transformed the glyph in several different ways, producing glyphs that were more similar to the numbers 4 or 3 than to the number 5.[2] It was from those characters that the Europeans finally came up with the modern 5, though from purely graphical evidence, it would be much easier to conclude that our modern 5 came from the Khmer. The Khmer glyph develops from the Kushana/Ândhra/Gupta numeral, its shape looking like a modern day version with an extended swirled 'tail' [G Ifrah, The Universal History of Numbers ISBN 1-86046-324-X]

While the shape of the 5 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in .

Religion and culture

Christian
Jewish
• The book of Psalms is arranged into five books, paralleling the Five Books of Moses.
• The Khamsa, an ancient symbol shaped like a hand with five fingers, is used as a protective amulet by Jews; that same symbol is also very popular in Arabic culture, known to protect from envy and the evil eye.
• The Torah contains five books—Genesis, Exodus, Leviticus, Numbers, and Deuteronomy—which are collectively called the Five Books of Moses, the Pentateuch (Greek for "five containers," referring to the scroll cases in which the books were kept), or Humash (חומש, Hebrew for "fifth").
Islamic
• Muslims pray to Allah five times a day
• In Islam, particularly Shia Islam, the Panjetan or the Five Holy Purified Ones are the members of Muhammad's family: Muhammad, Ali, Fatima, Hasan, and Husayn and is often symbolically represented by an image of the Khamsa.
• There are five basic "pillars" of Islam.
Sikh
• The five sacred Sikh symbols prescribed by Guru Gobind Singh are commonly known as Panj Kakars or the 'Five Ks' because they start with letter K representing Kakka in the Punjabi language. They are: Kesh (unshorn hair), Kangha (the comb), Kara (the steel bracelet), Kachh (the soldiers shorts), and Kirpan (the sword).
Discordianism
• In Discordianism, 5 is seen as a very important number. This is demonstrated in the Law of Fives, as well as in the Pentabarf, which contains five rules.
• Each page of the Principia Discordia —the primary religious document in Discordianism— is labeled with five digits.
Other
• According to ancient Greek philosophers such as Aristotle, the universe is made up of five classical elements: water, earth, air, fire, and ether. This concept was later adopted by Medieval alchemists and more recently by practitioners of Neo-Pagan religions such as Wicca.
• The pentagram, or five-pointed star, bears religious significance in various faiths including Baha'i, Christianity, Satanism, Taoism, Thelema and Wicca.
• In Cantonese, "five" sounds like the word "not" (symbol: 唔). When five appears in front of a lucky number, e.g. "58", the result is considered unlucky.
• In East Asian tradition, there are five elements: (water, fire, earth, wood, and metal). The Japanese names for the days of the week, Tuesday through Saturday, come from these elements via the identification of the elements with the five planets visible with the naked eye. Also, the traditional Japanese calendar has a five-day weekly cycle that can be still observed in printed mixed calendars combining Western, Chinese-Buddhist, and Japanese names for each weekday.
• Members of The Nation of Gods and Earths, a primarily African American religious organization, call themselves the "Five-Percenters" because they believe that only 5% of mankind is truly enlightened.

Music

• Albums or collections of music with 5 in the title:
• 5 is an album by Lamb.
• 5 is an album by Lenny Kravitz.
• 5 is an album by JJ Cale.
• 5th is an album by Lee Michaels.
• The 5% Album is a record by Lord Jamar; the title and subject matter are taken from the teachings of The Nation of Gods and Earths.

• Other Musical concepts:
• A Perfect fifth is the most consonant harmony, and is the basis for most western tuning systems.
• Modern musical notation uses a musical staff made of five horizontal lines.
• In harmonics – the fifth partial (or 4th overtone) of a fundamental has a frequency ratio of 5/1 to the frequency of that fundamental. This ratio corresponds to the interval of 2 octaves + a pure major third. Thus, the interval of 5/4 is the interval of the pure third. A major triad chord when played in just intonation (most often the case in a cappella vocal ensemble singing), will contain such a pure major third.
• The number of completed, numbered piano concertos of Ludwig van Beethoven, Sergei Prokofiev, and Camille Saint-Saëns.
• Using the Latin root, five musicians are called a quintet.
• The five notes per octave scale is the pentatonic scale.
• Five is the lowest possible number that can be the top number of a time signature with an asymmetric meter.

Film and television

Fast Five The fifth installment of the Fast and Furious series.

Technology

• 5 is the most common number of gears for automobiles with manual transmission.
• In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.
• On almost all devices with a numeric keypad such as telephones, computers, etc., the 5 key has a raised dot or raised bar to make dialing easier. Persons who are blind or have low vision find it useful to be able to feel the keys of a telephone. All other numbers can be found with their relative position around the 5 button (on computer keyboards, the 5 key of the numpad has the raised dot or bar, but the 5 key that shifts with % does not).
• On most telephones, the 5 key is associated with the letters J, K, and L, but on some of the BlackBerry phones, it is the key for G and H.
• The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.
• The resin identification code used in recycling to identify polypropylene.
• a pentamer is an oligomer composed of five sub-units.

Miscellaneous fields

Five can refer to:

The fives of all four suits in playing cards

References

1. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 61
2. ^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 394, Fig. 24.65

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