5 (number)

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This article discusses the number five. For the year 5 AD, see 5. For other uses of 5, see 5 (disambiguation).
5

0 1 2 3 4 5 6 7 8 9 →
Cardinal 5
five
Ordinal 5th
fifth
Numeral system quinary
Factorization prime
Divisors 1, 5
Roman numeral V
Roman numeral (Unicode) Ⅴ, ⅴ
Arabic ٥
Arabic (Urdu) ۵
Ge'ez ፭
Bengali ৫
Chinese numeral 五
Devanāgarī ५
Hebrew ה (He)
Khmer ៥
Thai ๕
prefixes penta-/pent- (from Greek)

quinque-/quinqu-/quint- (from Latin)
Binary 101
Octal 5
Duodecimal 5
Hexadecimal 5
Vigesimal 5
Look up five in
Wiktionary, the free dictionary.

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

Contents

[edit] Mathematics

Five is between 4 and 6 and is the third prime number, after 2 and 3, and before 7. Because it can be written as 2^(2^1)+1, five is classified as a Fermat prime. 5 is the third Sophie Germain prime, the first safe prime, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. 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 conjectured to be the only odd untouchable number.

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), ... (A030452 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.

5 and 6 form a Ruth-Aaron pair under either definition.

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=(2^2)+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.

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, as is the case with most primes, 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.

The number of terminal zeros in any number of numbers multiplied together will typically equal the number of 5's found in the prime factorization of the numbers. This means that multiplying the first 100 integers together will result in a number with 24 terminal zeros

Five is the only number for which the following identity holds: \sum_{i=1}^{5} \frac{1}{i} + \sum_{i=0}^{5} \frac{1}{i!} = 5


[edit] Numbering systems

[edit] List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
5 \times x 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 250 500 5000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5 \div x 5 2.5 1.\overline{6} 1.25 1 0.8\overline{3} 0.\overline{7}1428\overline{5} 0.625 0.\overline{5} 0.5 0.\overline{4}\overline{5} 0.41\overline{6} 0.\overline{3}8461\overline{5} 0.3\overline{5}7142\overline{8} 0.\overline{3}
x \div 5 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
5 ^ x\, 5 25 125 625 3125 15625 78125 390625 1953125 9765625 48828125 244140625 1220703125
x ^ 5\, 1 32 243 1024 3125 7776 16807 32768 59049 100000 161051 248832 371293

[edit] Evolution of the glyph

Image:Evolution5glyph.png

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 Kushana and Gupta Indians 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 look like a lowercase "h" rotated 180°. The Ghubar Arabs transformed the glyph in several different ways, coming up with glyphs that look more like 4s or 3s than 5s.[1] 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[citation needed].

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 Image:TextFigs256.png.

[edit] Science

[edit] Astronomy

[edit] Religion and culture

  • 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).
  • There are five basic "pillars" of Islam.
  • 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 including: Muhammad, Ali, Fatima, Hasan, Husayn and is often symbolically represented by an image of the Khamsa.
  • 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")
  • 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
  • According to some traditions of Maya mythology, we are now living in the Fifth World.
  • 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.
  • In some cultures there are five cardinal directions, including the center.
  • 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.
  • According to various mythologies, the universe is comprised of five classical elements: water, earth, air, fire and ether.
  • In Greek Orthodox Christian mysticism, the number 5 symbolizes the Holy Spirit as the bearer of all life. In the monastic tradition of Mount Athos there exists a "hymn" to the Holy Spirit composed entirely and solely of repetitions of the word "pente" (Greek for "five")
  • In Discordianism, 5 is seen as a very important number as demonstrated in the Law of Fives and The Pentabarf, which contains five rules. Each page of the Principia Discordia, the primary religious document in Discordianism, is also labeled with 5 digits.

[edit] Music

[edit] Sports

Jason Kidd wore the number five on his jersey while playing in the NBA.
Jason Kidd wore the number five on his jersey while playing in the NBA.
  • Kyle Busch's number in both the NEXTEL Cup Series and the Busch Series(no relation between the names). Also from 1994 until 2004 NASCAR champion Terry Labonte drove.
  • In Formula One, the number 5 & 6 cars traditionally belonged to the Williams team, until the end of the 1995 Formula One Season. It was most synonymous with Nigel Mansell in the late 80s and early 90s.
  • In professional Wrestling, if a wrestler grabs the ropes when he is in a submission hold, the attacking wrestler has up to a 5 count to break the hold until a disqualification is made. This is also the case for choking, grabbing the referee, or standing to the top of the turnbuckle. Contrary to belief, it is not a four count, as emphasized in WWE.
  • The number of players of a basketball team on the court at a given time.
  • Several players in the NBA have worn the number 5 on their jersey, including Hall of Fame caliber players Jason Kidd of the New Jersey Nets and most recently Kevin Garnett of the Boston Celtics. Bill Walton wore number 5 during the last few years of his career with the Boston Celtics.
  • Also used in basketball to represent the position of center.
  • The Olympic Games have five interlocked rings as their symbol, representing the number of inhabited continents represented by the Olympians (counting North America and South America as one continent).
  • The number of kyu (pupil) grades in judo
  • In rugby union, the number of the lock forward who usually jumps at number 4 in the line-out. It is also the number of points awarded for a try.
  • In rugby league, the number of the left wing, and also the number of tackles the attacking team has to score a try before the handover.
  • In baseball, five represents the third baseman's position.
  • 5 is the uniform number of Hall of Fame Baseball players Hank Aaron, Luke Appling, George Brett, Lou Boudreau, Hank Greenberg, Johnny Bench, Joe DiMaggio, and Brooks Robinson.
  • In hockey, the area between the goaltender's legs is known as the five-hole.
  • Heisman Winner Reggie Bush wore the number 5 in college at the University of Southern California.
  • Former Collingwood Magpies captain and member of the Team of the Century Nathan Buckley wore gurnsey number 5.

[edit] Technology

5 as a resin identification code, used in recycling.
  • The resin identification code used in recycling to identify polypropylene.
  • In radio communication, the term "Five by five" is used to indicate perfect signal strength and clarity.
  • The Pentium, coined by Intel Corporation, is a fifth-generation x86 architecture microprocessor.
  • On most telephones, the 5 key is associated with the letters J, K, and L, but on the BlackBerry it is the key for G and H.
  • 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).
  • 5 is the most common number of gears for automobiles with manual transmission.

[edit] Miscellaneous fields

International maritime signal flag for 5
International maritime signal flag for 5
The fives of all four suits in playing cards
The fives of all four suits in playing cards
See also: 5 (disambiguation)

Five is:

[edit] References

  1. ^ 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
  • Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 58 - 67