five

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

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.

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, 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), ... (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=(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 S_n 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, 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.

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 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.^[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 .

Science

• The atomic number of boron.
• The lightest atomic mass (the sum of protons and neutrons) for which no stable isotopes exist for any element.
• The number of appendages on most starfish, which exhibit pentamerism.
• The most destructive known hurricanes rate as Category 5 on the Saffir–Simpson Hurricane Scale.
• The most destructive known tornadoes rate an F-5 on the Fujita scale.

Astronomy

• Messier object M5, a magnitude 7.0 globular cluster in the constellation Serpens.
• The New General Catalogue object NGC 5, a magnitude 13 spiral galaxy in the constellation Andromeda.
• The Roman numeral V stands for dwarfs (main sequence stars) in the Yerkes spectral classification scheme.
• The Roman numeral V (usually) stands for the fifth-discovered satellite of a planet or minor planet (e.g. Jupiter V)
• The Saros number of the lunar eclipse series which began on -2581 October 8 and ended on -1084 March 24. The duration of Saros series 5 was 1496.5 years, and it contained 84 lunar eclipses.
• The Saros number of the solar eclipse series which began on April 4, 2720 BC and ended on May 24, 1422 BC. The duration of Saros series 5 was 1298.1 years, and it contained 73 solar eclipses.
• There are five Lagrangian points in a two-body system.

Biology

• Almost all amphibians, reptiles, and mammals which have fingers or toes have five of them on each extremity.^[why?]

Religion and culture

Judeo-Christian

• 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").
• 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").
• The Christian New Testament contains five foundational books, written by four authors: Matthew, Mark, Luke, John, and the Acts of the Apostles (written by the author of the Gospel according to Luke. The parallel with the Torah's five books is not likely accidental, as all the authors were most probably Jewish converts.

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 some traditions of Maya mythology, we are now living in the Fifth World.
• According to various mythologies, namely that of Wicca, the universe is made up of five classical elements: water, earth, air, fire, and ether.
• 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.
• In some cultures there are five cardinal directions, including the center.
• In India, Panchlothia, a surname, is based on the five mythological headless male warriors.

Money

• There are five cents in a U.S. and Canadian nickel, which is one twentieth of a dollar.
• The denomination of Canadian paper money bearing a portrait of Wilfrid Laurier, Canada's seventh Prime Minister.
• The denomination of U.S. paper money bearing a portrait of Abraham Lincoln, America's sixteenth President.

Music

• Songs or other compositions with 5 in the title:
• Five is the 13th track on The Burning Red album by heavy metal band Machine Head.
• 5 is a song from après les dancings album by Travis Bürki.
• Five Minutes Alone is a song by heavy metal group Pantera.
• Five Minutes Of Funk is a song by New York rapper Whodini.
• Take Five is a famous jazz standard composed by Paul Desmond. It counts five beats per bar.
• The Vogues song "Five-o'clock World" came in reference to the hours 9 to 5 (ending at 5 p.m.), which are the hours of a standard work day. There are also five working days (non-weekends) in a week.

• Albums or collections of music with 5 in the title:
• 5 is an album by Lenny Kravitz.

• Performers:
• #5 is the pseudonym of American musician Craig Jones, when performing with Slipknot
• Bands with "five" in their name include The Jackson 5, Maroon 5, We Five, Five for Fighting, The Click Five, MC5 (short for "Motor City Five"), Ben Folds Five, Five Man Electrical Band, The Five Keys, The Jive Five, The Count Five, The Five Satins, and The Dave Clark Five.
• Jurassic 5 is a hip hop crew whose second full length album was titled "Power in Numbers."
• Maroon 5 is a pop/rock band from Los Angeles, California, that has become popular thanks to songs such as "Harder To Breathe" and "This Love." The band won the Grammy Award for Best New Artist in 2005.
• The Five is the name of a 19th century Russian Group of nationalistic composers who included César Cui, Alexander Borodin, Mily Balakirev, Modest Mussorgsky, and Nikolai Rimsky-Korsakov.
• The name of the band The 5th Dimension implies that they are transcending beyond even the fourth dimension (time) into a new inner dimension.
• There was a British boy band called 5ive.

• 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.

Film and Television

• Babylon 5 is a science fiction television series created, produced and largely written by J. Michael Straczynski
• Odyssey 5 is a 2002 science fiction television series
• five is a television channel that broadcasts in the United Kingdom
• The Fifth Element is a 1997 science fiction film
• Five Go Mad in Dorset was the first of the long-running series of Comic Strip Presents... television comedy films
• Towards the end of the film Monty Python and the Holy Grail, the character of King Arthur repeatedly confuses the number five for the number three.
• The number 5 features in the television series Battlestar Galactica in regards to the Final Five cylons and the Temple of Five
• Johnny 5 is the lead character in the 1986 film Short Circuit

Literature

• The Famous Five is the name of a series of children's books by British writer Enid Blyton.

Sports

Jason Kidd wore the number five on his jersey while playing on the New Jersey Nets. He now plays on the Dallas Mavericks and wears the number two.

• 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).
• Five-a-side football is a variation of association football in which each team fields five players.
• Albert Pujols wears the number five for the St. Louis Cardinals baseball team.
• 5 is the uniform number of Hall of Fame Baseball players Luke Appling, George Brett, Lou Boudreau, Hank Greenberg, Johnny Bench, Joe DiMaggio, and Brooks Robinson.
• In baseball scorekeeping, the number five represents the third baseman's position.
• In basketball:
  • Several players in the NBA have worn the number 5 on their jersey, including Hall of Fame caliber players Jason Kidd of the Dallas Mavericks and most recently Kevin Garnett of the Boston Celtics. Kidd now wears the number two, but wears his old number on the USA men's national basketball team. Bill Walton wore number 5 during the last few years of his career with the Boston Celtics.
  • The number 5 is used to represent the position of center.
  • The number of players of a basketball team on the court at a given time.
• In Formula One racing, 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 hockey, the area between the goaltender's legs is known as the five-hole.
• 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.
• 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 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.
• The number of kyu (pupil) grades in judo.

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

International maritime signal flag for 5

Five is:

• An informal term for the British Security Service, MI5.
• Five babies born at one time are quintuplets. The most famous set of quintuplets were the Dionne quintuplets born in the 1930s.
• In the United States legal system, the Fifth Amendment to the United States Constitution can be referred to in court as "pleading the fifth", absolving the defendant from self-incrimination.
• Pentameter is verse with five repeating feet per line; iambic pentameter was the most popular form in Shakespeare.
• Quintessence, meaning 'fifth element', refers to the elusive fifth element that completes the basic four elements (water, fire, air, and earth)
• The designation of an Interstate Highway (Interstate 5) that runs from San Diego, California to Blaine, Washington. In addition, all major north-south Interstate Highways in the United States end in 5.
• The five basic tastes are sweet, salty, sour, bitter, and umami.
• In the computer game Riven, 5 is considered a holy number, and is a recurring theme throughout the game, appearing in hundreds of places, from the number of islands in the game, to the number of bolts on pieces of machinery.

The fives of all four suits in playing cards

• The Garden of Cyrus 1658 by Sir Thomas Browne is a Pythagorean Discourse based upon the number 5.
• The holy number of Discordianism, as dictated by the Law of Fives.
• The number of Justices on the Supreme Court of the United States necessary to render a majority decision.
• The number of dots in a quincunx.
• The number of permanent members with veto power on the United Nations Security Council.
• The number of points in a pentagram.
• The number of Korotkoff sounds when measuring blood pressure
• The drink Five Alive is named for its five ingredients.
• The Keating Five were five United States Senators accused of corruption in 1989.
• No. 5 is the name of the iconic fragrance created by Coco Chanel.
• The Committee of Five was delegated to draft the United States Declaration of Independence.
• The 5th U.S. President was James Monroe.

See also

Mathematics portal

References

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

External links

• My Favorite Numbers: 5, John C Baez