129.20.36.229: /* Role in decompositions */

2014-05-16T14:38:36Z

Role in decompositions

en>Quondum: /* Definitions */ spacing around '=', ellipsis

2014-01-02T21:13:41Z

Definitions: spacing around '=', ellipsis

New page

{{Refimprove|date=January 2009}}
{{Infobox number
| number = 25
| divisor = 1, 5, 25
}}
'''25''' ('''twenty-five''') is the [[natural number]] following [[24 (number)|24]] and preceding [[26 (number)|26]].

==In mathematics==
[[File:25.svg|thumb|25 is a square]]

It is a [[square number]], being [[5 (number)|5]]2 = 5 × 5. It is the smallest square that is also a sum of two (non-zero) squares: 25 = 32 + 42. Hence it often appears in illustrations of the [[Pythagorean theorem]].

25 is a [[centered octagonal number]], a [[centered square number]], and an [[automorphic number]].

25 percent(%) is equal to {{sfrac|4}}.

25 has an [[aliquot sum]] of 6 and number 6 is the first (or smallest) number to have an [[aliquot sequence]] that does not culminate in 0 through a [[prime number|prime]]. Twenty-five is the [[aliquot sum]] of three [[integers]]; 95, 119, and 143. Twenty-five is the second composite member of the 6-aliquot tree.

It is the smallest [[base 10]] [[Friedman number]] as it can be expressed by its own numbers: 52.

It is also a [[Cullen number]]. 25 is the smallest [[pseudoprime]] satisfying the congruence 7n = 7 mod n.

25 is the smallest [[aspiring number]] — a composite non-[[sociable number]] whose [[aliquot sequence]] does not terminate.

According to the [[Shapiro inequality]], 25 is the least odd integer n such that there exist <math>x_1, x_2, \dots, x_n</math> such that

:<math>\sum_{i=1}^{n} \frac{x_i}{x_{i+1}+x_{i+2}} < \frac{n}{2}</math>

where <math>x_{n+1}=x_1, x_{n+2}=x_2</math>.

Within base 10 one can readily test for divisibility by 25 by seeing if the last two digits of the number match 25, 50, 75 or 00.

25 and 49 are the only perfect squares in the following list:

13, '''25''', 37, '''49''', 511, 613, 715, 817, 919, 1021, 1123, 1225, 1327, 1429, etc.

The formula in this list can be described as <math>10^n * Z + (2Z + 1)</math> where n clearly depends on the number of digits in Z and in 2Z+1.

In base 30, 25 is a 1-[[automorphic number]] (displayed as the numeral 'P' or 'R' dependant on the chosen digit set), and in base 10 a 2-automorphic number.

==In science==
*The atomic number of [[manganese]]

==In religion==
*In '''[[Ezekiel]]'s vision of a new temple''': The number twenty-five is of cardinal importance in [[Ezekiel]]'s Temple Vision (in the Bible, [[Ezekiel]] chapters 40-48).

*In '''[[The Book of Revelation]]'s New International Version (1984)'''

*In Islam, there are twenty-five prophets mentioned in the Quran.

"Surrounding the throne were twenty-four other thrones, and seated on them were twenty-four elders. They were dressed in white and had crowns of gold on their heads."<ref>{{cite web|url=http://bible.cc/revelation/4-4.htm |title=Revelation 4:4 Surrounding the throne were twenty-four other thrones, and seated on them were twenty-four elders. They were dressed in white and had crowns of gold on their heads |publisher=Bible.cc |date= |accessdate=2013-05-03}}</ref> Which means that there were 25 thrones.

== In sports ==
*The size of the full roster on a [[Major League Baseball]] team for most of the season, except for regular-season games on or after September 1, when teams may expand their roster to no more than 40 players.
*In baseball, the number 25 is typically reserved for the best slugger on the team. Examples include [[Mark McGwire]], [[Barry Bonds]], and [[Mark Teixeira]].
*The number of points needed to win a set in volleyball under rally scoring rules (except for the fifth set), so long as the losing team's score is two less than the winning team's score (i.e., if the winning team scores 25 points, the losing team can have no more than 23 points)
*In [[College football|U.S. college football]], schools that are members of [[Division I (NCAA)|NCAA Division I]] [[Football Bowl Subdivision|FBS]] are allowed to provide [[athletic scholarship]]s to a maximum of 25 new football players (i.e., players who were not previously receiving scholarships) each season.

==In other fields==
[[Image:I-25.svg|right|100px]]

'''Twenty five''' is:
*The part of the name of [[LSD-25]] molecule
*The number of years of marriage marked in a silver [[wedding anniversary]].
*The minimum age of candidates for election to the [[United States House of Representatives]]. "Under 25" provides a common cut-off point for designating [[youth]].
*The number of cents in a [[Quarter (United States coin)|quarter]].
*The usual [[Transmission control protocol|TCP]] port for [[SMTP]].
*The designation of [[United States]] [[Interstate 25]], a freeway that runs from [[New Mexico]] to [[Wyoming]]
*The designation of the [[M25 motorway|M25]] London Orbital motorway
*Municipal Okrug 25, until March, 2010, name of [[Knyazhevo Municipal Okrug]] in Kirovsky District of [[Saint Petersburg]], Russia
*The (critical) number of Florida electoral votes for the [[U.S. presidential election, 2000|2000 U.S. presidential election]]
*The name of the national board game of [[India]] ([[Pachisi]] — Hindi for 25)
*"25", a song by Veruca Salt from their 1994 album ''[[American Thighs]]''
*"25th Floor", a song by Patti Smith Group from their 1978 album ''[[Easter (Patti Smith Group album)|Easter]]''
*"twentyfive", design studio in the Czech Republic
*[[Twenty Five (album)|Twenty Five]] is the name of a 2006 [[George Michael]] compilation celebrating 25 years in the music business (1981–2006)
*The total number of playable characters in ''[[Mario Kart Wii]]'' and ''[[Super Smash Bros. Melee]]''.
*"25 boy" (read as "two-five boy"), in Cantonese Chinese, is a slang term meaning "traitor" as used in the Chinese movie [[Over the Edge (film)|Over the Edge]].
*The per-second frame rate of the [[PAL]] video standard
*The number of the French department [[Doubs (department)|Doubs]]
*[[25 random things about me]], an [[Internet meme]] utilizing Facebook's Notes feature

==Slang names==
* Pony (British slang for £25)<ref>Evans, I.H., ''Brewer's Dictionary of Phrase and Fable'', 14th ed., Cassell, 1990, ISBN 0-304-34004-9</ref>

==References==
{{commonscat}}
{{reflist}}

{{Integers|zero}}

[[Category:Integers|2 5]]

Idempotent element - Revision history

129.20.36.229: /* Role in decompositions */

en>Quondum: /* Definitions */ spacing around '=', ellipsis