14

"14th" redirects here. For the electronic music duo, see 14th (band).

← 13 14 15 →
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Cardinal	fourteen
Ordinal	14th (fourteenth)
Numeral system	tetradecimal
Factorization	2 × 7
Divisors	1, 2, 7, 14
Greek numeral	ΙΔ´
Roman numeral	XIV
Greek prefix	tetrakaideca-
Latin prefix	quattuordec-
Binary	11102
Ternary	1123
Senary	226
Octal	168
Duodecimal	1212
Hexadecimal	E16
Hebrew numeral	י"ד
Babylonian numeral	𒌋𒐘

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

Mathematics

Fourteen is the seventh composite number.

Properties

14 is the third distinct semiprime, being the third of the form $2\times q$ (where $q$ is a higher prime). More specifically, it is the first member of the second cluster of two discrete semiprimes (14, 15); the next such cluster is (21, 22), members whose sum is the fourteenth prime number, 43.

14 has an aliquot sum of 8, within an aliquot sequence of two composite numbers (14, 8, 7, 1, 0) in the prime 7-aliquot tree.

14 is the third companion Pell number and the fourth Catalan number. It is the lowest even $$

 
   
     
       n
     
   
   {\displaystyle n}
 

$n$ for which the Euler totient $$

 
   
     
       φ
       (
       x
       )
       =
       n
     
   
   {\displaystyle \varphi (x)=n}
 

$\varphi (x)=n$ has no solution, making it the first even nontotient.

According to the Shapiro inequality, 14 is the least number $$

 
   
     
       n
     
   
   {\displaystyle n}
 

$n$ such that there exist $$

 
   
     
       
         x
         
           1
         
       
     
   
   {\displaystyle x_{1}}
 

$x_{1}$, $$

 
   
     
       
         x
         
           2
         
       
     
   
   {\displaystyle x_{2}}
 

$x_{2}$, $$

 
   
     
       
         x
         
           3
         
       
     
   
   {\displaystyle x_{3}}
 

$x_{3}$, where:

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

with $x_{n+1}=x_{1}$ and $x_{n+2}=x_{2}.$

A set of real numbers to which it is applied closure and complement operations in any possible sequence generates 14 distinct sets. This holds even if the reals are replaced by a more general topological space; see Kuratowski's closure-complement problem.

There are fourteen even numbers that cannot be expressed as the sum of two odd composite numbers:

$\{2,4,6,8,10,12,14,16,20,22,26,28,32,38\}$

where 14 is the seventh such number.

Polygons

14 is the number of equilateral triangles that are formed by the sides and diagonals of a regular six-sided hexagon. In a hexagonal lattice, 14 is also the number of fixed two-dimensional triangular-celled polyiamonds with four cells.

14 is the number of elements in a regular heptagon (where there are seven vertices and edges), and the total number of diagonals between all its vertices.

There are fourteen polygons that can fill a plane-vertex tiling, where five polygons tile the plane uniformly, and nine others only tile the plane alongside irregular polygons.

The fundamental domain of the Klein quartic is a regular hyperbolic 14-sided tetradecagon, with an area of $$

 
   
     
       8
       π
     
   
   {\displaystyle 8\pi }
 

.

The Klein quartic is a compact Riemann surface of genus 3 that has the largest possible automorphism group order of its kind (of order 168) whose fundamental domain is a regular hyperbolic 14-sided tetradecagon, with an area of $8\pi$ by the Gauss-Bonnet theorem.

Solids

Several distinguished polyhedra in three dimensions contain fourteen faces or vertices as facets:

• The cuboctahedron, one of two quasiregular polyhedra, has 14 faces and is the only uniform polyhedron with radial equilateral symmetry.
• The rhombic dodecahedron, dual to the cuboctahedron, contains 14 vertices and is the only Catalan solid that can tessellate space.
• The truncated octahedron contains 14 faces, is the permutohedron of order four, and the only Archimedean solid to tessellate space.
• The dodecagonal prism, which is the largest prism that can tessellate space alongside other uniform prisms, has 14 faces.
• The Szilassi polyhedron and its dual, the Császár polyhedron, are the simplest toroidal polyhedra; they have 14 vertices and 14 triangular faces, respectively.
• Steffen's polyhedron, the simplest flexible polyhedron without self-crossings, has 14 triangular faces.

A regular tetrahedron cell, the simplest uniform polyhedron and Platonic solid, is made up of a total of 14 elements: 4 edges, 6 vertices, and 4 faces.

• Szilassi's polyhedron and the tetrahedron are the only two known polyhedra where each face shares an edge with each other face, while Császár's polyhedron and the tetrahedron are the only two known polyhedra with a continuous manifold boundary that do not contain any diagonals.
• Two tetrahedra that are joined by a common edge whose four adjacent and opposite faces are replaced with two specific seven-faced crinkles will create a new flexible polyhedron, with a total of 14 possible clashes where faces can meet.^pp.10-11,14 This is the second simplest known triangular flexible polyhedron, after Steffen's polyhedron.^p.16 If three tetrahedra are joined at two separate opposing edges and made into a single flexible polyhedron, called a 2-dof flexible polyhedron, each hinge will only have a total range of motion of 14 degrees.^p.139

14 is also the root (non-unitary) trivial stella octangula number, where two self-dual tetrahedra are represented through figurate numbers, while also being the first non-trivial square pyramidal number (after 5); the simplest of the ninety-two Johnson solids is the square pyramid $J_{1}.$ There are a total of fourteen semi-regular polyhedra, when the pseudorhombicuboctahedron is included as a non-vertex transitive Archimedean solid (a lower class of polyhedra that follow the five Platonic solids).

Fourteen possible Bravais lattices exist that fill three-dimensional space.

G₂

The exceptional Lie algebra G₂ is the simplest of five such algebras, with a minimal faithful representation in fourteen dimensions. It is the automorphism group of the octonions $\mathbb {O}$, and holds a compact form homeomorphic to the zero divisors with entries of unit norm in the sedenions, $\mathbb {S}$.

Riemann zeta function

The floor of the imaginary part of the first non-trivial zero in the Riemann zeta function is $14$, in equivalence with its nearest integer value, from an approximation of $14.1347251417\ldots$

In science

Chemistry

14 is the atomic number of silicon, and the approximate atomic weight of nitrogen. The maximum number of electrons that can fit in an f sublevel is fourteen.

In religion and mythology

Christianity

According to the Gospel of Matthew "there were fourteen generations in all from Abraham to David, fourteen generations from David to the exile to Babylon, and fourteen from the exile to the Messiah" (Matthew 1, 17).

It can also signify the Fourteen Holy Helpers.

Mythology

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

The number 14 was regarded as connected to Šumugan and Nergal.

In other fields

Fourteen is:

• The number of days in a fortnight.
• The Fourteenth Amendment to the United States Constitution gave citizenship to those of African descent, in a post-Civil War (Reconstruction) measure aimed at restoring the rights of slaves.
• The number of lines in a sonnet.
• The Piano Sonata No. 14, also known as Moonlight Sonata, is one of the most famous piano sonatas composed by Ludwig van Beethoven.
• Auto racing legend A.J. Foyt most often carried the #14 on his cars, and as his primary number since the early 1970s.
• MLB Hall of Famer Ernie Banks wore the #14 while playing for the Chicago Cubs, with the team retiring the number in his honor in 1982.

References

Bibliography

• Wiggermann, Frans A. M. (1998), "Nergal A. Philological", Reallexikon der Assyriologie, retrieved 2022-03-06

Fourteen or 14 may refer to:

• 14 (number), the natural number following 13 and preceding 15
• One of the years 14 BC, AD 14, 1914, 2014

Music

• 14th (band), a British electronic music duo
• 14 (David Garrett album), 2013
• 14, an unreleased album by Charli XCX
• "14" (song), a 2007 song by Paula Cole from Courage
• "Fourteen", a 2000 song by The Vandals from Look What I Almost Stepped In...

Other uses

• Fourteen (film), a 2019 American film directed by Dan Sallitt
• Fourteen (play), a 1919 play by Alice Gerstenberg
• Fourteen (manga), a 1990 manga series by Kazuo Umezu
• 14 (novel), a 2013 science fiction novel by Peter Clines
• The 14, a 1973 British drama film directed by David Hemmings
• Fourteen, West Virginia, United States, an unincorporated community
• Lot Fourteen, redevelopment site in Adelaide, South Australia, previously occupied by the Royal Adelaide Hospital
• "The Fourteen", a nickname for NASA Astronaut Group 3
• Fourteen Words, a phrase used by white supremacists and neo-Nazis
• 14 Irene, an asteroid in the asteroid belt
• Rover 14, various mid-sized cars produced by Rover
• Hillman 14, a family car

See also

• 1/4 (disambiguation)
• Fourteener, a high peak in United States mountains
• Fourteener (poetry), a line of 14 syllables
• Fourteen 14, an Italian Eurodance project
• List of highways numbered 14
• Onefour, an Australian rap group
• Onefour, Alberta, a research substation in Canada

14 est le plus petit anti-indicateur pair, c'est-à-dire le plus petit entier pair strictement positif n'appartenant pas à l'image de l'indicatrice d'Euler.

Chronologies

Campagnes de Germanicus en 14

Données clés

11 12 13  14  15 16 17 Décennies : -10 -0 0  10  20 30 40 Siècles : -IIe -Ier  Ier  IIe IIIe Millénaires : -IIe -Ier  Ier  IIe IIIe

Calendriers

Romain Chinois Grégorien Julien Hébraïque Hindou Hégirien Persan Républicain

L'année 14 est une année commune qui commence un lundi.

Événements

Portrait en bronze de l'Empereur Tibère. Héritier imposé par la volonté du fondateur du régime, il ne sait comment se faire respecter. Il assure cependant la consolidation du principat. Il traite d’abord avec le Sénat et élargit ses compétences, puis, dans la seconde partie de son règne, inaugure une politique de condamnations arbitraires, use de la délation et de la calomnie pour se débarrasser d’aristocrates jugés dangereux.

• 11 mai : le recensement dénombre 4 937 000 citoyens romains.
• Été : Tibère part de Rome pour l’Illyrie pour finir de la pacifier. Auguste, affaibli, l’accompagne jusqu’à Bénévent, puis se rend à Astura, sur la côte du Latium, pour s’embarquer pour la Campanie. Il assiste à Capri aux jeux traditionnels des éphèbes, à Naples aux jeux gymniques ou quinquennaux. À Nole, il se trouve subitement indisposé. Il rappelle Tibère en toute hâte. Tibère le trouve fort malade, mais peut avoir avec lui un entretien secret.
• 19 août : décès d'Auguste à Nola, premier empereur romain.
• 17 septembre : Auguste est divinisé. Début du règne de Tibère, empereur romain (fin en 37).
• Septembre-octobre : les légions romaines du Rhin et Pannonie se révoltent après la mort de l'empereur Auguste (Legio XXI Rapax, Legio V Alaudae, Legio I Germanica, Legio XVI Gallica, Legio XIV Gemina, etc.). Germanicus et Drusus répriment la rébellion.

• Début des campagnes de Germanicus en Germanie (fin en 16). Il passe le Rhin et ravage le territoire des Marses, des Tubantes, des Bructères et des Usipètes.
• Séjan devient préfet du prétoire en association avec son père Seius Strabo, chevalier d'origine étrusque (fin en 31). Il intervient en Pannonie aux côtés de Drusus.
• Tibère supprime les comices électoraux et en transfère les prérogatives à l’assemblée sénatoriale, développe la valeur légale des sénatus-consultes puis érige le Sénat en haute cour de justice compétente dans des causes importantes, comme la sûreté de l’État ou les procès concernant les membres de l’ordre sénatorial.
• À Rome, 153 846 personnes bénéficient de distribution gratuite de céréales.
• Famine en Chine. Les paysans deviennent anthropophages.

Naissances en 14

• Marcus Junius Silanus, consul romain.
• Pétrone, écrivain latin.

Décès en 14

• 19 août : Auguste, empereur romain.
• Julia, fille d'Auguste.
• Agrippa Postumus, fils d'Agrippa et de Julia, petit-fils et fils adoptif d'Auguste.
• Paullus Fabius Maximus, consul romain.

Lien externe

• L’année 14 sur le site de la Bibliothèque nationale de France

Le 14 décembre est l'anniversaire de ma Maman. — capi