14 (number)

← 13
15 →
14
Cardinal fourteen
Ordinal 14th
(fourteenth)
Numeral system tetradecimal
Factorization 2 \cdot 7
Divisors 1, 2, 7, 14
Roman numeral XIV
Binary 11102
Octal 168
Duodecimal 1212
Hexadecimal E16

14 (fourteen  /fɔərˈtiːn/) is the natural number following 13 and preceding 15. In speech, the numbers 14 and 40 are often confused. When carefully enunciated, they differ in which syllable is stressed: 14 /fɔərˈtiːn/ ( listen) vs 40 /ˈfɔrti/.[1] However, in dates such as 1492 or when contrasting numbers in the teens, such as 13, 14, 15, the stress shifts to the first syllable: 14 /ˈfɔərtiːn/.

Contents

In mathematics

Fourteen is a composite number, its divisors being 1, 2, 7 and 14.

14 is the 3rd discrete semiprime ( 2 . 7 ) and the 3rd member of the (2.q) discrete semiprime family. The number following 14—15 is itself a discrete semiprime and this is the first such pair of discrete semiprimes. The next example is the pair commencing 21.

The aliquot sum σ(n) of 14 is 10, also a discrete semiprime and this is again the first example of a discrete semiprime having an aliquot sum in the same form. 14 has an aliquot sequence of 6 members ( 14,10,8,7,1,0) 14 is the third composite number in the 7-aliquot tree.

Fourteen is itself the Aliquot sum of two numbers; the discrete semiprime 22, and the square number 196.

It is the base of the tetradecimal notation.

In base fifteen and higher bases (such as hexadecimal), fourteen is represented as E.

Fourteen is the sum of the first three squares, which makes it a square pyramidal number.

This number is the lowest even n for which the equation φ(x) = n has no solution, making it the first even nontotient (see Euler's totient function).

14 is a Catalan number, the only semiprime among all Catalan numbers.

Take a set of real numbers and apply the closure and complement operations to it in any possible sequence. At most 14 distinct sets can be generated in this way. This holds even if the reals are replaced by a more general topological space. See Kuratowski's closure-complement problem.

Fourteen is a Keith number in base 10: 1, 4, 5, 9, 14, 23, 37, 60, 97, 157...

Fourteen is an open meandric number.

Fourteen is a Companion Pell number.

According to the Shapiro inequality 14 is the least number n such that there exist x_1, x_2, \dots, x_n such that

\sum_{i=1}^{n} \frac{x_i}{x_{i%2B1}%2Bx_{i%2B2}} < \frac{n}{2}

where x_{n%2B1}=x_1, x_{n%2B2}=x_2.

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

The cuboctahedron, the truncated cube, and the truncated octahedron each have fourteen faces. The rhombic dodecahedron, which tessellates 3-dimensional space and is the dual of the cuboctahedron, has fourteen vertices. The truncated octahedron, which also tessellates 3-dimensional space, is the only permutohedron.

In science

Chemistry

Astronomy

In religion

Age 14

In sports

White Pride symbol

Among White Nationalists, 14 signifies the "Fourteen Words"—"We must secure the existence of our people and a future for white children"—attributed to David Lane. Often found in combination with 88 (1488, 8814, 14/88, etc.).

In other fields

Fourteen is:

Historical years

14 A.D., 14 B.C., 1914 etc.

References

  1. ^ The vowels of the syllables four- and for- are identical in many dialects, such as General American and younger speakers of Received Pronunciation.