14 (number)

Natural number, composite number 14 (disambiguation) 14 tetradecimal 1, 2, 7, 14 tetrakaideca- quattuordec- Hebrew numeral י"ד Babylonian numeral 𒌋𒐘 14 (fourteen) is the natural number following 13 and preceding 15. fourteen Mathematics Properties 14 is the third distinct semiprime,A001358 being the third of the form (where 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 10, within an aliquot sequence of two composite numbers (14, 10, 8, 7, 1, 0) in the prime 7-aliquot tree. 14 is the third companion Pell number and the fourth Catalan number.https://oeis.org/A002203 Sloane's A002203 : Companion Pell numbers The On-Line Encyclopedia of Integer Sequences OEIS Foundation 2016-06-01https://oeis.org/A000108 Sloane's A000108 : Catalan numbers The On-Line Encyclopedia of Integer Sequences OEIS Foundation 2016-06-01 It is the lowest even for which the Euler totient has no solution, making it the first even nontotient.https://oeis.org/A005277 Sloane's A005277 : Nontotients The On-Line Encyclopedia of Integer Sequences OEIS Foundation 2016-06-01 According to the Shapiro inequality, 14 is the least number such that there exist , , , where:Troesch B. A. https://www.ams.org/journals/mcom/1985-45-171/S0025-5718-1985-0790653-0/S0025-5718-1985-0790653-0.pdf On Shapiro's Cyclic Inequality for N = 13 Mathematics of Computation 45 171 July 1975 199 10.1090/S0025-5718-1985-0790653-0 free 790653 51803624 0593.26012 with and A set of real numbers to which it is applied closure and complement operations in any possible sequence generates 14 distinct sets. Kelley John John L. Kelley https://archive.org/details/generaltopology0000kell registration General Topology Springer New York June 27, 1975 1955 57 9780387901251 10277303 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: where 14 is the seventh such number.A118081 Even numbers that can't be represented as the sum of two odd composite numbers. 2024-08-03 Polygons There are fourteen equilateral triangles formed by the sides and diagonals of a regular six-sided hexagon.A238822 Number of equilateral triangles bounded by the sides and diagonals of a regular 3n-gon. 2024-05-05 In a hexagonal lattice, there are fourteen fixed two-dimensional triangular-celled polyiamonds with four cells.A001420 Number of fixed 2-dimensional triangular-celled animals with n cells (n-iamonds, polyiamonds) in the 2-dimensional hexagonal lattice. 2024-05-15 There are fourteen 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.Branko Grünbaum Branko Grünbaum Geoffrey Shepard G.C. Shephard Tilings by Regular Polygons November 1977 http://www.maa.org/sites/default/files/images/upload_library/22/Allendoerfer/1978/0025570x.di021102.02p0230f.pdf Mathematics Magazine 50 5 Taylor & Francis, Ltd. 231 10.2307/2689529 2689529 123776612 0385.51006 2016-03-03 2023-01-18 https://web.archive.org/web/20160303235526/http://www.maa.org/sites/default/files/images/upload_library/22/Allendoerfer/1978/0025570x.di021102.02p0230f.pdf dead Baez John C. John Carlos Baez https://blogs.ams.org/visualinsight/2015/02/01/pentagon-decagon-packing/ Pentagon-Decagon Packing AMS Blogs American Mathematical Society February 2015 2023-01-18 190px|thumb|The fundamental domain of the Klein quartic is a regular hyperbolic 14-sided tetradecagon, with an area of . 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. Solids thumb|14 is a square pyramidal number. thumb|14 is a stella octangula number. 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.Coxeter H.S.M. Harold Scott MacDonald Coxeter https://archive.org/details/regularcomplexpo0000coxe registration Regular Polytopes Chapter 2: Regular polyhedra Dover 3rd New York 1973 18–19 0-486-61480-8 798003 The rhombic dodecahedron, dual to the cuboctahedron, contains 14 vertices and is the only Catalan solid that can tessellate space.Williams Robert https://archive.org/details/geometricalfound0000will/page/168/mode/2up registration The Geometrical Foundation of Natural Structure: A Source Book of Design Chapter 5: Polyhedra Packing and Space Filling Dover Publications, Inc. New York 1979 168 9780486237299 5939651 108409770 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. Szilassi Lajos Structural Topology 69–80 Regular toroids http://www-iri.upc.es/people/ros/StructuralTopology/ST13/st13-06-a3-ocr.pdf 13 1986 0605.52002 Császár Ákos Ákos Császár http://www.diale.org/pdf/csaszar.pdf https://web.archive.org/web/20170918064243/http://www.diale.org/pdf/csaszar.pdf 2017-09-18 A polyhedron without diagonals Acta Scientiarum Mathematicarum (Szeged) 140–142 13 1949 Steffen's polyhedron, the simplest flexible polyhedron without self-crossings, has 14 triangular faces.Lijingjiao Iila Tachi Tomohiro Guest Simon D. 1 https://www.repository.cam.ac.uk/bitstream/handle/1810/279138/IASS2015_paper%20Author%20Accepted%20Version.pdf?sequence=1&isAllowed=y Optimizing the Steffen flexible polyhedron Proceedings of the International Association for Shell and Spatial Structures (Future Visions Symposium) Amsterdam IASS 2015 10.17863/CAM.26518 125747070 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.Li Jingjiao 2018 Flexible Polyhedra: Exploring finite mechanisms of triangulated polyhedra https://core.ac.uk/download/pdf/151178534.pdf Ph.D. Thesis University of Cambridge, Department of Engineering xvii, 1-156 10.17863/CAM.18803 free 204175310 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);A007588 Stella octangula numbers 2023-01-18 A000330 Square pyramidal numbers 2023-01-18 the simplest of the ninety-two Johnson solids is the square pyramid 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. 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).Grünbaum Branko Branko Grünbaum An enduring error Elemente der Mathematik 64 3 89–101 European Mathematical Society Helsinki 2009 10.4171/EM/120 free 2520469 1176.52002 119739774 Hartley Michael I. Williams Gordon I. Representing the sporadic Archimedean polyhedra as abstract polytopes Discrete Mathematics 310 12 Elsevier Amsterdam 1835–1844 2010 10.1016/j.disc.2010.01.012 free 0910.2445 2009arXiv0910.2445H 2610288 1192.52018 14912118 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). Fourteen possible Bravais lattices exist that fill three-dimensional space.A256413 Number of n-dimensional Bravais lattices. 2023-01-18 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 , and holds a compact form homeomorphic to the zero divisors with entries of unit norm in the sedenions, . Baez John C. John Baez The Octonions Bulletin of the American Mathematical Society New Series 39 2 186 2002 https://math.ucr.edu/home/baez/octonions/node14.html 10.1090/S0273-0979-01-00934-X math/0105155 1886087 586512 1026.17001 Moreno Guillermo The zero divisors of the Cayley–Dickson algebras over the real numbers 1998 Bol. Soc. Mat. Mexicana Series 3 4 1 13–28 q-alg/9710013 1997q.alg....10013G 1625585 20191410 1006.17005 Riemann zeta function The floor of the imaginary part of the first non-trivial zero in the Riemann zeta function is ,A013629 Floor of imaginary parts of nontrivial zeros of Riemann zeta function. 2024-01-16 in equivalence with its nearest integer value,A002410 Nearest integer to imaginary part of n-th zero of Riemann zeta function. 2024-01-16 from an approximation of A058303 Decimal expansion of the imaginary part of the first nontrivial zero of the Riemann zeta function. 2024-01-16 Odlyzko Andrew Andrew Odlyzko The first 100 (non trivial) zeros of the Riemann Zeta function [AT&T Labs] https://www-users.cse.umn.edu/~odlyzko/zeta_tables/zeros2 Andrew Odlyzko: Home Page UMN CSE 2024-01-16 In religion and mythology Christianity There is a fourteen-point silver star marking the traditional spot of Jesus’ birth in the Basilica of the Nativity in Bethlehem. According to the genealogy of Jesus in 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). Islam In Islam, 14 has a special significance because of the Fourteen Infallibles who are especially revered and important in Twelver Shi'ism. They are all considered to be infallible by Twelvers alongside the Prophets of Islam, however these fourteen are said to have a greater significance and closeness to God. These fourteen include: Prophet Muhammad (SAWA) His daughter, Lady Fatima (SA) Her husband, Imam Ali (AS) His son, Imam Hasan (AS) His brother, Imam Husayn (AS) His son, Imam Ali al-Sajjad (AS) His son, Imam Muhammad al-Baqir (AS) His son, Imam Ja'far al-Sadiq (AS) His son, Imam Musa al-Kazim (AS) His son, Imam Ali al-Rida (AS) His son, Imam Muhammad al-Jawad (AS) His son, Imam Ali al-Hadi (AS) His son, Imam Hasan al-Askari (AS) His son, Imam Muhammad al-Mahdi (AJTFS) Mythology The number 14 was linked to Šumugan and Nergal.Wiggermann 1998 222 In other fields There are fourteen days in a fortnight. Notes References Bibliography Frans A. M. Wiggermann Nergal A. Philological Reallexikon der Assyriologie http://publikationen.badw.de/en/rla/index#8358 1998 2022-03-06 zero Category:Integers Category:14 (number)