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

← 13 14 15 →
Numeral systemtetradecimal
Factorization2 × 7
Divisors1, 2, 7, 14
Greek numeralΙΔ´
Roman numeralXIV
Greek prefixtetrakaideca-
Latin prefixquattuordec-

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

In mathematics edit

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

Fourteen is the seventh composite number. It is specifically, the third distinct Semiprime,[1] it also being the 3rd 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) to the Prime in the 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).

It is the lowest even   for which the equation   has no solution, making it the first even nontotient.[2]

A set of real numbers to which it is applied closure and complement operations in any possible sequence generates 14 distinct sets.[3] This holds even if the reals are replaced by a more general topological space; see Kuratowski's closure-complement problem.

14 is the third stella octangula number, and the second square pyramidal number.[4][5]

14 is also the fourth Companion Pell number, and the fifth Catalan number.[6][7]

According to the Shapiro inequality, 14 is the least number   such that there exist  ,  ,  , where:[8]


with   and  

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.[9][10]

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

The regular tetrahedron, 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.[16]pp.10-11,14 This is the second simplest known triangular flexible polyhedron, after Steffen's polyhedron.[16]p.16 Furthermore, 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.[16]p.139

There are fourteen possible Bravais lattices that fill three-dimensional space.[17]

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   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  , and holds a compact form homeomorphic to the zero divisors with entries of unit norm in the sedenions,  .[18][19]

In science edit

Chemistry edit

Astronomy edit

In religion and mythology edit

Christianity edit

Islam edit

Hinduism edit

Mythology edit

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.[21]

Age 14 edit

  • 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.[22]
  • In some countries, it is the age of sexual consent.

In sports edit

In other fields edit

Fourteen is:

See also edit

References edit

  1. ^ Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  3. ^ Kelley, John (1955). General Topology. New York: Van Nostrand. p. 57. ISBN 9780387901251. OCLC 10277303.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A007588 (Stella octangula numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-18.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-18.
  6. ^ "Sloane's A002203 : Companion Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  7. ^ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  8. ^ Troesch, B. A. (July 1975). "On Shapiro's Cyclic Inequality for N = 13" (PDF). Mathematics of Computation. 45 (171): 199. doi:10.1090/S0025-5718-1985-0790653-0. MR 0790653. S2CID 51803624. Zbl 0593.26012.
  9. ^ Grünbaum, Branko; Shepard, Geoffrey (November 1977). "Tilings by Regular Polygons" (PDF). Mathematics Magazine. Taylor & Francis, Ltd. 50 (5): 231. doi:10.2307/2689529. JSTOR 2689529. S2CID 123776612. Zbl 0385.51006.
  10. ^ Baez, John C. (February 2015). "Pentagon-Decagon Packing". AMS Blogs. American Mathematical Society. Retrieved 2023-01-18.
  11. ^ 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.
  12. ^ 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. p. 168. ISBN 9780486237299. OCLC 5939651. S2CID 108409770.
  13. ^ Szilassi, Lajos (1986). "Regular toroids" (PDF). Structural Topology. 13: 69–80. Zbl 0605.52002.
  14. ^ Császár, Ákos (1949). "A polyhedron without diagonals" (PDF). Acta Scientiarum Mathematicarum (Szeged). 13: 140–142. Archived from the original (PDF) on 2017-09-18.
  15. ^ Lijingjiao, Iila; et al. (2015). "Optimizing the Steffen flexible polyhedron" (PDF). Proceedings of the International Association for Shell and Spatial Structures (Future Visions Symposium). Amsterdam: IASS. doi:10.17863/CAM.26518. S2CID 125747070.
  16. ^ a b c 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.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A256413 (Number of n-dimensional Bravais lattices.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-01-18.
  18. ^ Baez, John C. (2002). "The Octonions". Bulletin of the American Mathematical Society. New Series. 39 (2): 186. arXiv:math/0105155. doi:10.1090/S0273-0979-01-00934-X. MR 1886087. S2CID 586512. Zbl 1026.17001.
  19. ^ 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, arXiv:q-alg/9710013, Bibcode:1997q.alg....10013G, MR 1625585, S2CID 20191410, Zbl 1006.17005
  20. ^ "Places where Lord Ram stayed during 14 years of exile". Archived from the original on 2018-12-26. Retrieved 2018-03-19.
  21. ^ Wiggermann 1998, p. 222.
  22. ^ Zimring, Franklin (2015). Juvenile Justice in Global Perspective. NYU Press. p. 21. ISBN 978-1-4798-9044-6. Extract of page 21
  23. ^ Bowley, Roger. "14 and Shakespeare the Numbers Man". Numberphile. Brady Haran. Archived from the original on 2016-02-01. Retrieved 2016-01-03.
  24. ^ 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 edit