14 (number)

← 13 14 15 →
← 10 11 12 13 14 15 16 17 18 19 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	fourteen
Ordinal	14th (fourteenth)
Numeral system	tetradecimal
Factorization	2 × 7
Divisors	1, 2, 7, 14
Roman numeral	XIV
Greek prefix	tetrakaideca-
Latin prefix	quattuordec-
Binary	11102
Ternary	1123
Quaternary	324
Quinary	245
Senary	226
Octal	168
Duodecimal	1212
Hexadecimal	E16
Vigesimal	E20
Base 36	E36

14 (fourteen /fɔərˈtiːn/) is the natural number following 13 and preceding 15.

In speech, the numbers 14 and 40 are often confused. When carefully enunciated, they differ in which syllable is stressed: 14 ⁱ/fɔərˈtiːn/ vs 40 /ˈfɔːrti/.^[1] In relation to the word "four" (4), 14 is spelled "fourteen". In a 24-hour clock, the fourteenth hour is in conventional language called two or two o'clock.

In mathematics

Fourteen is a composite number, its divisors being 1, 2, 7 and 14.

14 is the third discrete semiprime (2 × 7) and the 3rd member of the (2·q) discrete semiprime family. The number following 14—15—is itself a discrete semiprime and this is the first such pair of discrete semiprimes. The next example is the pair commencing 21.

The aliquot sum σ(n) of 14 is 10, also a discrete semiprime and this is again the first example of a discrete semiprime having an aliquot sum in the same form. 14 has an aliquot sequence of 6 members (14,10,8,7,1,0) 14 is the third composite number in the 7-aliquot tree.

Fourteen is itself the aliquot sum of two numbers; the discrete semiprime 22, and the square number 169.

Fourteen is the base of the tetradecimal notation.

In base fifteen and higher bases (such as hexadecimal), fourteen is represented as E.

Fourteen is the sum of the first three squares, which makes it a square pyramidal number.^[2]

This number is the lowest even n for which the equation φ(x) = n has no solution, making it the first even nontotient (see Euler's totient function).^[3]

14 is a Catalan number, the only semiprime among all Catalan numbers.^[4]

Take a set of real numbers and apply the closure and complement operations to it in any possible sequence. At most 14 distinct sets can be generated in this way. This holds even if the reals are replaced by a more general topological space. See Kuratowski's closure-complement problem.

Fourteen is a Keith number in base 10: 1, 4, 5, 9, 14, 23, 37, 60, 97, 157...^[5]

Fourteen is an open meandric number.

Fourteen is a Companion Pell number.^[6]

According to the Shapiro inequality 14 is the least number n such that there exist x₁, x₂, …, x_n such that

$\sum _{{i=1}}^{{n}}{\frac {x_{i}}{x_{{i+1}}+x_{{i+2}}}}<{\frac {n}{2}}$

where x_{n + 1} = x₁, x_{n + 2} = x₂.

There are fourteen possible Bravais lattices that fill three-dimensional space.

The cuboctahedron, the truncated cube, and the truncated octahedron each have fourteen faces. The rhombic dodecahedron, which tessellates 3-dimensional space and is the dual of the cuboctahedron, has fourteen vertices. The truncated octahedron, which also tessellates 3-dimensional space, is the only permutohedron.

In science

Chemistry

• The atomic number of silicon
• The approximate atomic weight of nitrogen
• The maximum number of electrons that can fit in an f sublevel

Astronomy

• Messier object M14, a magnitude 9.5 globular cluster in the constellation Ophiuchus
• The New General Catalogue object [NGC 14, a magnitude 12.5 irregular galaxy in the constellation Pegasus
• The Saros number of the solar eclipse series which began on July 31, 2568 B.C. and ended on February 6, 1035 B.C. The duration of Saros series 14 was 1532.5 years, and it contained 86 solar eclipses
• The Saros number of the lunar eclipse series which began on June 1, 2230 B.C. and ended on July 19, 932 B.C. The duration of Saros series 14 was 1298.1 years, and it contained 73 lunar eclipses.

In religion and mythology

Christianity

• According to the Gospel of Matthew "there were fourteen generations in all from Abraham to David, fourteen from David to the exile to Babylon, and fourteen from the exile to the Messiah". (Matthew 1, 17)
• The number of Stations of the Cross.
• The Fourteen Holy Helpers were a group of saints formerly venerated together by Roman Catholics.

Mormonism

• The age of Joseph Smith when he witnessed the First Vision.

Islam

• The number of muqatta'at in the Quran.
• The number of Infalliables (Masoomeen) in Shia Ithna-Asheri Islam.

Hinduism

The number of years of Rama's exile in the forests in Hinduism.

Mythology

The number of pieces the body of Osiris was torn into by his fratricidal brother Set.

Age 14

• Age 14 is the earliest that the emancipation of minors can occur in the U.S.
• Minimum age a person can purchase, rent or buy tickets to a 14A rated movie in Canada without an adult. Ratings are provincial, so ratings may vary. A movie can be 14A in one or some provinces and PG in other provinces. A movie can also be rated 14A in one or some provinces and 18A in other provinces. Quebec has a different rating system for films.
• Youngest age in Canada a person can watch a 14+ rated show without consent from a legal guardian.
• Minimum age at which one can view, rent, purchase, or buy tickets to an 18A rated movie with an accompanying adult in the Canadian provinces of the Maritimes and Manitoba.
• Minimum age at which one can work in many U.S states. Some require parental consent while others don't.
• Minimum age at which one can work in most Australian states with parent's consent.
• Minimum age at which one can drive a vehicle in the U.S. with a driver's license (with supervision of an adult over 18 years of age, and with a valid, unmarked driver's license, and at least 365 days of experience driving an actual automobile)
• The minimum age limit to drive a 50cc motorbike in Italy.
• The most common age of criminal responsibility in Europe.^[7]

In sports

• The G-14 is a now-defunct union of eighteen football clubs.
• In Association football the number 14 was the number worn by and associated with Johan Cruyff.^[8] In 2007, to honour his 60th birthday, his first club AFC Ajax decided to never use it again.
• In rugby union:
  • The starting right wing wears the 14 shirt.
  • The Top 14 is the highest-level league in French rugby union.
  • The Southern Hemisphere competition now known as Super Rugby was known from 2006 through 2010, an era in which it had 14 teams, as Super 14.
• In the NASCAR Sprint Cup Series, the #14 car is currently owned by Stewart Haas Racing. Since 2009, it has been driven by team co-owner Tony Stewart.
• In Formula 1 the number 14 is used by Fernando Alonso, the 2005 and 2006 world champion, for McLaren F1
• In Thoroughbred horse racing:
  • The following major races have a maximum field of 14 runners:
    • The Preakness Stakes and Belmont Stakes, the final two legs of the U.S. Triple Crown.
    • All of the Breeders' Cup races except for the Dirt Mile, Juvenile Fillies, and Juvenile Fillies Turf (limited to 12).
• In golf, a player can have no more than 14 clubs in the bag.
• The jersey number 14 has been retired by several North American sports teams in honor of past playing greats or other key figures:
  • In Major League Baseball:
    • The Boston Red Sox, for Hall of Famer Jim Rice.
    • The Chicago Cubs, for Hall of Famer Ernie Banks.
    • The Cincinnati Reds, for Pete Rose, who also managed the team.
    • The Cleveland Indians, for Hall of Fame player Larry Doby, who also managed the team.
    • The Minnesota Twins, for Kent Hrbek.
    • The New York Mets, for Gil Hodges, who both played for and managed the team.
    • The Philadelphia Phillies, for Hall of Famer Jim Bunning.
    • The St. Louis Cardinals, for Ken Boyer.
  • In the NBA:
    • The Boston Celtics, for Hall of Famer Bob Cousy.
    • The Golden State Warriors, for Tom Meschery, who played for the team in its past incarnations as the Philadelphia and San Francisco Warriors.
    • The Milwaukee Bucks, for Jon McGlocklin.
    • The Portland Trail Blazers, for Lionel Hollins.
    • The Sacramento Kings, for Hall of Famer Oscar Robertson, who played for the team when it was known as the Cincinnati Royals.
    • The Utah Jazz, for Jeff Hornacek.
  • In the NFL:
    • The Cleveland Browns, for Hall of Famer Otto Graham.
    • The Green Bay Packers, for Hall of Famer Don Hutson.
    • The New York Giants, for Hall of Famer Y. A. Tittle.
    • The San Diego Chargers, for Hall of Famer Dan Fouts.
  • In the NHL:
    • The Buffalo Sabres, for René Robert.

In other fields

Fourteen is:

• The number of days in a fortnight.
• In traditional British units of weight, the number of pounds in a stone.
• A number 'encoded' in much of the music of Johann Sebastian Bach. Bach may have considered this number a sort of signature, since given A = 1, B = 2, C = 3, etc., then B + A + C + H = 14. (See also 41)
• The number of points outlined by president Woodrow Wilson for reconstructing a new Europe following World War I, see Fourteen Points.
• The number of Enigma Variations composed by Edward Edgar.
• The number of favored rows in the Roman theater for members of the equestrian order according to the lex Roscia theatralis issued in 67 BC.
• The section that you go to when you die in the Grailquest books.
• The number of legs on a woodlouse, as well as on Hallucigenia.
• A common designation for the thirteenth floor in many buildings for superstitious reasons.
• There are 14 British Overseas Territories of the United Kingdom.
• The number of lines in a sonnet.^[9]
• The Number 14 airship by Alberto Santos Dumont that was used to test the aerodynamics of his 14-bis airplane.
• The number of the French department Calvados.
• XIV is a Storage server manufactured by IBM. It goes by name of "XIV" and is pronounced as the separate letters "X", "I", "V".
• The Piano Sonata No. 14, also known as Moonlight Sonata, is one of the most famous piano sonatas composed by Ludwig van Beethoven.
• A symbol of infinity in "The House of Asterion" ("Spanish: La casa de Asterión", 1947) by Jorge Luis Borges.^[10]
• The Fourteen Words are a phrase used by white nationalists.
• Nuestra Familia is a gang that uses "XIV" as their symbol because the 14th letter of the Spanish alphabet is "N".

References

1. The vowels of the syllables four- and for- are identical in many dialects, such as General American and younger speakers of Received Pronunciation.
2. "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
3. "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
4. "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
5. "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
6. "Sloane's A002203 : Companion Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
7. Zimring, Franklin (2015). Juvenile Justice in Global Perspective. NYU Press. p. 21. ISBN 978-1-4798-9044-6. Extract of page 21
8. "Johan Cruyff: Netherlands great dies of cancer aged 68". BBC Online. Retrieved 24 March 2016.
9. Bowley, Roger. "14 and Shakespeare the Numbers Man". Numberphile. Brady Haran.
10. Jean Ann Bowman, Jorge Luis Borges: A study of criticism in the United States, M.A. thesis submitted to and approved by the Graduate Faculty of Texas Tech University, May 1987.