14 (number)

Short description: Natural number, composite number

Short description: Natural number

| <- 13  | 14 |  15 ->

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← 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
Greek numeral| ΙΔ´
Roman numeral| XIV
Greek prefix| tetrakaideca-
Greek 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) is a natural number following 13 and preceding 15.

In relation to the word "four" (4), 14 is spelled "fourteen".

## Contents

* 1 In mathematics
* 2 In science
* 2.1 Chemistry
* 2.2 Astronomy
* 3 In religion and mythology
* 3.1 Christianity
* 3.2 Islam
* 3.3 Hinduism
* 3.4 Mythology
* 4 Age 14
* 5 In sports
* 6 In white supremacy
* 7 In other fields
* 8 See also
* 9 Notes
* 10 References
* 10.1 Bibliography

## In mathematics

Fourteen is the seventh composite number. It is the lowest even n for which the Euler totient φ(x)=n has no solution, making it the first even nontotient.[1]

It is specifically, the third distinct semiprime,[2] being the third of the form 2×q, where q is a higher prime.

It 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 first member of the first cluster of two discrete semiprimes (14, 15) the next such cluster is (21, 22).

14 is also the third Companion Pell number, and the fourth Catalan number.[3][4]

According to the Shapiro inequality, 14 is the least number n such that there exist x1, x2, x3, where:[5]

∑i=1nxixi+1+xi+2<n2,

with xn+1=x1 and xn+2=x2.

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.[6][7]

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.[8]
* The rhombic dodecahedron, dual to the cuboctahedron, contains 14 vertices and is the only Catalan solid that can tessellate space.[9]
* 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.[10][11]
* Steffen's polyhedron, the simplest flexible polyhedron without self-crossings, has 14 triangular faces.[12]

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.[13]pp.10-11,14 This is the second simplest known triangular flexible polyhedron, after Steffen's polyhedron.[13]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.[13]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);[14][15] the simplest of the ninety-two Johnson solids is the square pyramid J1.[lower-alpha 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).[16][17][lower-alpha 2]

There are fourteen possible Bravais lattices that fill three-dimensional space.[18]

The fundamental domain of the Klein quartic is a regular hyperbolic 14-sided tetradecagon, with an area of 8π.

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 8π by the Gauss-Bonnet theorem.

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 𝕆, and holds a compact form homeomorphic to the zero divisors with entries of unit norm in the sedenions, 𝕊.[19][20]

A set of real numbers to which it is applied closure and complement operations in any possible sequence generates 14 distinct sets.[21] This holds even if the reals are replaced by a more general topological space; see Kuratowski's closure-complement problem.

The floor of the imaginary part of the first non-trivial zero in the Riemann zeta function is 14,[22] in equivalence with its nearest integer value,[23] from an approximation of 14.1347251417…[24][25]

## 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
* Group 14 elements in the periodic table.

### 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

## 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)
* The number of Stations of the Cross observed by some Christian denominations.
* The Fourteen Holy Helpers were a group of saints formerly venerated together by Roman Catholics.

### Islam

* The number of Muqattaʿat in the Quran.
* Significant for Twelver Shia Muslims who follow the Fourteen Infallibles.

### Hinduism

* The number of years of Rama's exile in the forest with Sita and Lakshman.[26]

### Mythology

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

The number of sacrificial victims of the Minotaur.

The number 14 was regarded as connected to Šumugan and Nergal.[27]

## Age 14

* 14 is the earliest age 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.
* The U.S. TV Parental Guidelines has a rating called "TV-14" which strongly recommends parental guidance for children under the age of fourteen watching the program.
* 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. Parental consent may be required, depending on the state.
* Minimum age at which one can drive a vehicle in the U.S. with a driver's license (with the 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.[28]
* In some countries, it is the age of sexual consent.

## In sports

* In American football, the National Football League playoffs have involved 14 teams since the 2020 season.
* In golf, a player can have no more than 14 clubs in the bag.
* In rugby union, the starting right wing wears the 14 shirt
* In pool:
* The pool ball 14 is the 14th in pool and its color is green.

## In white supremacy

White supremacists use the number 14 as a reference to the Fourteen Words coined by David Lane, a prominent white supremacist.[29]

This number is often associated with the number 88 (e.g. 14/88, 14-88, or 1488) that is an abbreviation for the Nazi salute Heil Hitler.[30]

## 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.
* In traditional British units of weight, the number of pounds in a stone.
* 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 Elgar.
* 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 one goes to when one dies 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.[31]
* The Number 14 airship by Alberto Santos Dumont 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,[32] itself a reference to the 14 sacrificial victims of the Minotaur.
* Nuestra Familia is a gang that uses "XIV" as their symbol because the 14th letter of the Spanish alphabet is "N".
* The room number on the top floor of the hospital where Oliver Hardy is visited by Stan Laurel in the movie County Hospital (1932).
* In the epic fantasy series A Song of Ice and Fire, the Fourteen Flames are a chain of volcanoes that stretch across the Valyrian peninsula.
* There are 14 books in the main sequence of the epic fantasy series The Wheel of Time by Robert Jordan.
* The number of years Edmond Dantes spent imprisoned in the Chateau d'If in Alexandre Dumas' The Count of Monte Cristo.
* Unlike most other mammal species which commonly have 20 digits (toes), 14 is the number of digits of the guinea pig or domestic guinea pig (Cavia porcellus), also known as the cavy or domestic cavy (/ˈkeɪvi/).

## See also

* List of highways numbered 14

## Notes

1. ↑ Furthermore, the square pyramid can be attached to uniform and non-uniform polyhedra (such as other Johnson solids) to generate fourteen other Johnson solids: J8, J10, J15, J17, J49, J50, J51, J52, J53, J54, J55, J56, J57, and J87.
2. ↑ Where the tetrahedron — which is self-dual, inscribable inside all other Platonic solids, and vice-versa — contains fourteen elements, there exist thirteen uniform polyhedra that contain fourteen faces (U09, U76i, U08, U77c, U07), vertices (U76d, U77d, U78b, U78c, U79b, U79c, U80b) or edges (U19).

## References

1. ↑ "Sloane's A005277 : Nontotients". OEIS Foundation. https://oeis.org/A005277.
2. ↑ Sloane, N. J. A., ed. "Sequence A001358". OEIS Foundation. https://oeis.org/A001358.
3. ↑ "Sloane's A002203 : Companion Pell numbers". OEIS Foundation. https://oeis.org/A002203.
4. ↑ "Sloane's A000108 : Catalan numbers". OEIS Foundation. https://oeis.org/A000108.
5. ↑ Troesch, B. A. (July 1975). "On Shapiro's Cyclic Inequality for N = 13". Mathematics of Computation 45 (171): 199. doi:10.1090/S0025-5718-1985-0790653-0. https://www.ams.org/journals/mcom/1985-45-171/S0025-5718-1985-0790653-0/S0025-5718-1985-0790653-0.pdf.
6. ↑ Grünbaum, Branko; Shepard, Geoffrey (November 1977). "Tilings by Regular Polygons". Mathematics Magazine (Taylor & Francis, Ltd.) 50 (5): 231. doi:10.2307/2689529. http://www.maa.org/sites/default/files/images/upload_library/22/Allendoerfer/1978/0025570x.di021102.02p0230f.pdf.
7. ↑ Baez, John C. (February 2015). "Pentagon-Decagon Packing". American Mathematical Society. https://blogs.ams.org/visualinsight/2015/02/01/pentagon-decagon-packing/.
8. ↑ Coxeter, H.S.M. (1973). "Chapter 2: Regular polyhedra". Regular Polytopes (3rd ed.). New York: Dover. pp. 18–19. ISBN 0-486-61480-8. OCLC 798003. https://archive.org/details/regularcomplexpo0000coxe.
9. ↑ Williams, Robert (1979). "Chapter 5: Polyhedra Packing and Space Filling". The Geometrical Foundation of Natural Structure: A Source Book of Design. New York: Dover Publications, Inc.. pp. 168. ISBN 9780486237299. OCLC 5939651. https://archive.org/details/geometricalfound0000will/page/168/mode/2up.
10. ↑ Szilassi, Lajos (1986). "Regular toroids". Structural Topology 13: 69–80. http://www-iri.upc.es/people/ros/StructuralTopology/ST13/st13-06-a3-ocr.pdf.
11. ↑ Császár, Ákos (1949). "A polyhedron without diagonals". Acta Scientiarum Mathematicarum (Szeged) 13: 140–142. http://www.diale.org/pdf/csaszar.pdf.
12. ↑ Lijingjiao, Iila et al. (2015). "Optimizing the Steffen flexible polyhedron". Proceedings of the International Association for Shell and Spatial Structures (Future Visions Symposium) (Amsterdam: IASS). doi:10.17863/CAM.26518. https://www.repository.cam.ac.uk/bitstream/handle/1810/279138/IASS2015_paper Author Accepted Version.pdf?sequence=1&isAllowed=y.
13. ↑ 13.0 13.1 13.2 Li, Jingjiao (2018). Flexible Polyhedra: Exploring finite mechanisms of triangulated polyhedra (PDF) (Ph.D. Thesis). University of Cambridge, Department of Engineering. pp. xvii, 1–156\. doi:10.17863/CAM.18803. S2CID 204175310.
14. ↑ Sloane, N. J. A., ed. "Sequence A007588 (Stella octangula numbers)". OEIS Foundation. https://oeis.org/A007588. Retrieved 2023-01-18.
15. ↑ Sloane, N. J. A., ed. "Sequence A000330 (Square pyramidal numbers)". OEIS Foundation. https://oeis.org/A000330. Retrieved 2023-01-18.
16. ↑ Grünbaum, Branko (2009). "An enduring error". Elemente der Mathematik (Helsinki: European Mathematical Society) 64 (3): 89–101. doi:10.4171/EM/120. https://ems.press/content/serial-article-files/2342.
17. ↑ Hartley, Michael I.; Williams, Gordon I. (2010). "Representing the sporadic Archimedean polyhedra as abstract polytopes". Discrete Mathematics (Amsterdam: Elsevier) 310 (12): 1835–1844. doi:10.1016/j.disc.2010.01.012. Bibcode: 2009arXiv0910.2445H. https://www.sciencedirect.com/science/article/pii/S0012365X10000257.
18. ↑ Sloane, N. J. A., ed. "Sequence A256413 (Number of n-dimensional Bravais lattices.)". OEIS Foundation. https://oeis.org/A256413. Retrieved 2023-01-18.
19. ↑ Baez, John C. (2002). "The Octonions". Bulletin of the American Mathematical Society. New Series 39 (2): 186. doi:10.1090/S0273-0979-01-00934-X. https://math.ucr.edu/home/baez/octonions/node14.html.
20. ↑ Moreno, Guillermo (1998), "The zero divisors of the Cayley–Dickson algebras over the real numbers", Bol. Soc. Mat. Mexicana, Series 3 4 (1): 13–28, Bibcode: 1997q.alg....10013G
21. ↑ Kelley, John (1955). General Topology. New York: Van Nostrand. p. 57. ISBN 9780387901251. OCLC 10277303. https://archive.org/details/generaltopology0000kell.
22. ↑ Sloane, N. J. A., ed. "Sequence A013629 (Floor of imaginary parts of nontrivial zeros of Riemann zeta function.)". OEIS Foundation. https://oeis.org/A013629. Retrieved 2024-01-16.
23. ↑ Sloane, N. J. A., ed. "Sequence A002410 (Nearest integer to imaginary part of n-th zero of Riemann zeta function.)". OEIS Foundation. https://oeis.org/A002410. Retrieved 2024-01-16.
24. ↑ Sloane, N. J. A., ed. "Sequence A058303 (Decimal expansion of the imaginary part of the first nontrivial zero of the Riemann zeta function.)". OEIS Foundation. https://oeis.org/A058303. Retrieved 2024-01-16.
25. ↑ Odlyzko, Andrew. "The first 100 (non trivial) zeros of the Riemann Zeta function [AT&T Labs"]. UMN CSE. https://www-users.cse.umn.edu/~odlyzko/zeta_tables/zeros2.
26. ↑ "Places where Lord Ram stayed during 14 years of exile". https://medium.com/@reachostaff/places-where-lord-ram-stayed-during-14-years-of-exile-98e48f3ea6c8.
27. ↑ Wiggermann 1998, p. 222.
28. ↑ Zimring, Franklin (2015). Juvenile Justice in Global Perspective. NYU Press. p. 21. ISBN 978-1-4798-9044-6. https://books.google.com/books?id=V-8WCgAAQBAJ. Extract of page 21
29. ↑ "14". https://www.adl.org/resources/hate-symbol/14.
30. ↑ "Racist Skinhead Glossary | Southern Poverty Law Center". https://www.splcenter.org/fighting-hate/intelligence-report/2015/racist-skinhead-glossary.
31. ↑ Bowley, Roger. "14 and Shakespeare the Numbers Man". Numberphile. Brady Haran. http://www.numberphile.com/videos/14_shakespeare.html.
32. ↑ 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.

### Bibliography

* Wiggermann, Frans A. M. (1998)

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