32 (number) (nonfiction)

32 (thirty-two) is the natural number following 31 and preceding 33.

In mathematics

32 is the smallest number n with exactly 7 solutions to the equation φ(x) = n. It is also the sum of Euler's totient function for the first ten integers.

The fifth power of two, 32 is also a Leyland number since 24 + 42 = 32.

32 is the ninth happy number.

32 = 11 + 22 + 33

In science

• The atomic number of germanium
• The freezing point of water at standard atmospheric pressure in degrees Fahrenheit

Astronomy

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

In music

• 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 Pāli Canon in the Theravada Buddhist tradition, the Digha Nikaya, describes the appearance of the historical Buddha with a list of 32 physical characteristics.
• 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.
• 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.

Miscellaneous

• The number of teeth of a full set of teeth in an adult human, including wisdom teeth
• The size of a databus in bits: 32-bit
• The size, in bits, of certain integer data types, used in computer 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
• Article 32 of the UCMJ concerns pre-trial investigations. Such a hearing is often called an "article 32 hearing"
• Sometimes considered to be the occult opposite of number 23[citation needed]
• The caliber .32 ACP
• The number of pages in the average comic book (not including the cover)[citation needed]
• The number of the French department Gers
• The traditional 32 counties of Ireland

See also

• Euler's totient function (nonfiction) - a function which counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek letter phi as φ(n) or ϕ(n), and may also be called Euler's phi function. In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal to 1. The integers k of this form are sometimes referred to as totatives of n.
• Happy number (nonfiction) - a natural number in a given number base {\displaystyle b}b that eventually reaches 1 when iterated over the perfect digital invariant function for {\displaystyle p=2}p=2. Those numbers that do not end in 1 are {\displaystyle b}b-unhappy numbers (or {\displaystyle b}b-sad numbers). The origin of happy numbers is not clear. Happy numbers were brought to the attention of Reg Allenby (a British author and senior lecturer in pure mathematics at Leeds University) by his daughter, who had learned of them at school. However, they "may have originated in Russia"
• Leyland number (nonfiction) - a number of the form {\displaystyle x^{y}+y^{x}}x^y + y^x

where x and y are integers greater than 1. They are named after the mathematician Paul Leyland. The first few Leyland numbers are: 8, 17, 32, 54, 57, 100, 145, 177, 320, 368, 512, 593, 945, 1124 (sequence A076980 in the OEIS). The requirement that x and y both be greater than 1 is important, since without it every positive integer would be a Leyland number of the form x1 + 1x. Also, because of the commutative property of addition, the condition x ≥ y is usually added to avoid double-covering the set of Leyland numbers (so we have 1 < y ≤ x).

• Natural number (nonfiction) - numbers used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country"). In common mathematical terminology, words colloquially used for counting are "cardinal numbers" and words connected to ordering represent "ordinal numbers". The natural numbers can, at times, appear as a convenient set of codes (labels or "names"); that is, as what linguists call nominal numbers, forgoing many or all of the properties of being a number in a mathematical sense.
• Power of two (nonfiction) - a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent. In a context where only integers are considered, n is restricted to non-negative values, so we have 1, 2, and 2 multiplied by itself a certain number of times. Because two is the base of the binary numeral system, powers of two are common in computer science. Written in binary, a power of two always has the form 100…000 or 0.00…001, just like a power of ten in the decimal system.

• 32 (number) @ Wikipedia