32 (number)

: ${\displaystyle 22\times 24=528}$.

32 is also a Leyland number expressible in the form ${\displaystyle x^{y}+y^{x}}$, where:^[5][b]

$${\displaystyle 32=2^{4}+4^{2}.}$$

The eleventh Mersenne number is the first to have a prime

$${\displaystyle 2047=32^{2}+(31\times 33)=1024+1023=2^{11}-1.}$$

numbering

$${\displaystyle 2^{32}-1=3\cdot 5\cdot 17\cdot 257\cdot 65\;537=4\;294\;967\;295.}$$

The first 32 rows of Pascal's triangle read as single binary numbers represent the 32 divisors that belong to this number, which is also the number of sides of all odd-sided constructible polygons with simple tools alone (if the monogon is also included).^[10]

There are also a total of 32 uniform colorings to the 11 regular and semiregular tilings.^[11]

There are 32 three-dimensional crystallographic point groups^[12] and 32 five-dimensional crystal families,^[13] and the maximum determinant in a 7 by 7 matrix of only zeroes and ones is 32.^[14] In sixteen dimensions, the sedenions generate a non-commutative loop ${\displaystyle \mathbb {S} _{L}}$ of

lattices that exists in twenty-four dimensions, or the single ${\displaystyle \mathrm {E} _{8}}$ lattice in eight dimensions (these lattices only exist for dimensions ${\displaystyle d\propto 8}$). Furthermore, the 32nd dimension is the first dimension that holds non-critical even unimodular lattices that do not interact with a

${\displaystyle f_{\alpha }(r)=e^{-\alpha {r}}}$

${\displaystyle r}$

${\displaystyle \alpha >0}$

32 is the furthest point in the set of natural numbers ${\displaystyle \mathbb {N} _{0}}$ where the ratio of primes (2, 3, 5, ..., 31) to non-primes (0, 1, 4, ..., 32) is ${\displaystyle {\tfrac {1}{2}}.}$^[d]

In science

• The atomic number of germanium
• The
  degrees Fahrenheit
• In the Standard Model of particle physics, there are 32 degrees of freedom among the leptons and all bosons that interact with them (including the graviton, which is generally expected to exist, and assuming there are no right-handed neutrinos)^{[citation needed]}

Astronomy

• magnitude 9.0 galaxy in the constellation Andromeda which is a companion to M31
  .
• The
  NGC 32, a star in the constellation Pegasus

• A thirty-second note or demisemiquaver is a note played for 1/32 of the duration of a whole note
• The number of completed, numbered piano
  sonatas by Ludwig van Beethoven
• "32 Footsteps", a song by They Might Be Giants
• "The Chamber of 32 Doors", a song by Genesis, from their 1974 concept album The Lamb Lies Down on Broadway
• "32", a song on Mr. Mister's debut album I Wear the Face
• "32", a song by electro-rock group Carpark North
• "Thirty Two", a song by Van Morrison on the album New York Sessions '67
• ThirtyTwo is the fourth album by English band Reverend and the Makers
• "32 Pennies", a song on Warrant's 1989 debut album Dirty Rotten Filthy Stinking Rich
• The number of rays in the Japanese Rising Sun on the cover of Incubus' 2006 album Light Grenades
• "32 Ways To Die", a song on
  Sum41's album Half Hour of Power
• The shortened pseudonym of UK rapper Wretch 32

In religion

In the Kabbalah, there are 32 Kabbalistic Paths of Wisdom. This is, in turn, derived from the 32 times of the Hebrew names for God, Elohim appears in the first chapter of Genesis.

One of the central texts of the

The Hindu scripture Mudgala Purana also describes Ganesha as taking 32 forms.

In sports

• In chess, the total number of black squares on the board, the total number of white squares, and the total number of pieces (black and white) at the beginning of the game.
• The number of teams in the National Football League.
• The number of teams in the National Hockey League.
• In association football:
  • The FIFA World Cup final tournament has featured 32 men's national teams from 1998 through 2022, after which the field will expand to 48.
  • The FIFA Women's World Cup final tournament will feature 32 national teams starting with the next edition in 2023.
  • The ball used in association football is most often made with 32 panels of leather or synthetic material.

In other fields

Thirty-two could also refer to:

• The number of teeth of a full set of teeth in an adult human, including
  wisdom teeth
• The size of a
  32-bit
• The size, in bits, of certain
  representations of numbers
• IPv4 uses 32-bit (4-byte
  ) addresses
• ASCII and Unicode code point for space
• The
  code for international direct dial
  phone calls to Belgium
• In the title Thirty-Two Short Films About Glenn Gould, starring Colm Feore
• The Article 32 of the
  UCMJ
  concerns pre-trial investigations. Such a hearing is often called an "Article 32 hearing"
• The caliber .32 ACP
• The number of the French department Gers
• The traditional 32 counties of Ireland

Notes