14 (number)

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

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

Look up fourteen in Wiktionary, the free dictionary.

Mathematics

Fourteen is the seventh composite number. It is specifically, the third distinct semiprime,^[1] being the third of the form ${\displaystyle 2\times q}$ (where ${\displaystyle q}$ is a higher prime). More specifically, it is the first member of the second cluster of two discrete

Properties

14 is the third Companion Pell number, and the fourth Catalan number.^[2][3] It is the lowest even ${\displaystyle n}$ for which the

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

According to the Shapiro inequality, 14 is the least number ${\displaystyle n}$ such that there exist ${\displaystyle x_{1}}$, ${\displaystyle x_{2}}$, ${\displaystyle x_{3}}$, where:^[5]

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

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

A set of real numbers to which it is applied closure and complement operations in any possible sequence generates 14 distinct sets.^[6] This holds even if the reals are replaced by a more general topological space; see Kuratowski's closure-complement problem.

Polygons

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.^[7][8]

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 ${\displaystyle 8\pi }$ by the

Solids

Several distinguished

• The
  radial equilateral symmetry.^[9]
• The rhombic dodecahedron, dual to the cuboctahedron, contains 14 vertices and is the only Catalan solid that can tessellate space.^[10]
• 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.^[11][12]
• Steffen's polyhedron, the simplest flexible polyhedron without self-crossings, has 14 triangular faces.^[13]

A regular

• 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.^{[14]pp.10-11,14} This is the second simplest known triangular flexible polyhedron, after Steffen's polyhedron.^[14]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.^[14]p.139

14 is also the root (non-unitary) trivial

${\displaystyle J_{1}.}$

G₂

The

octonions

${\displaystyle \mathbb {O} }$, and holds a compact form

, ${\displaystyle \mathbb {S} }$.

Riemann zeta function

The

is ${\displaystyle 14}$,

${\displaystyle 14.1347251417\ldots }$

In science

Chemistry

14 is the

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)

Islam

The number of Muqattaʿat in the Quran.

Mythology

The number of pieces the body of

The number 14 was regarded as connected to Šumugan and Nergal.^[26]

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.^[27]
• The Piano Sonata No. 14, also known as Moonlight Sonata, is one of the most famous piano sonatas composed by Ludwig van Beethoven.

Notes