List of refractive indices: Difference between revisions

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| number = 81
| divisor = 1, 3, 9, 27, 81
}}
'''81''' ('''eighty-one''') is the [[natural number]] following [[80 (number)|80]] and preceding [[82 (number)|82]].
 
==In mathematics==
Eighty-one is the [[square number|square]] of [[9 (number)|9]] and the fourth power of [[3 (number)|3]]. Like all powers of three, 81 is a [[perfect totient number]]. It is a [[heptagonal number]] and a [[centered octagonal number]]. It is also a [[tribonacci number]], and an [[open meandric number]]. 81 is the ninth member of the [[Mian-Chowla sequence]].
 
In base 10, it is a [[Harshad number]], and one of three non-trivial numbers (the other two are [[1458 (number)|1458]] and [[1729 (number)|1729]]) which, when its digits are added together, produces a sum which, when multiplied by its reversed self, yields the original number:
 
: 8 + 1 = 9
: 9 &times; 9 = 81
 
(although this case is somewhat degenerate, as the sum has only a single digit).
 
{{wiktionary|eighty-one}}
 
The inverse of 81 is 0.012345679 recurring, missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base ''b'',
:<math>\frac{1}{\left(b-1\right)^2} = 0.\overline{012\cdots(b-4)(b-3)(b-1)},</math>
omitting only the digit ''b''&minus;2.
 
==In astronomy==
*[[Messier object]] [[Messier 81|M81]], a [[visual magnitude|magnitude]] 8.5 [[spiral galaxy]] in the [[constellation]] [[Ursa Major]], also known as [[Bode's Galaxy]], and the first of what is known as the [[M81 Group]] of galaxies
*The [[New General Catalogue]] object [[NGC 81]], a [[spiral galaxy]] in the constellation [[Andromeda (constellation)|Andromeda]]
*The [[Saros number]] of the [[solar eclipse]] series which began on -0322 May 12 and ended on 0958 June. The duration of Saros series 81 was 1280.1 years, and it contained 72 solar eclipses. Further, the number of [[lunar eclipse]] series which began on -0020 February 19 and ended on 1296  April 19. The duration of Saros series 81 was 1316.2 years, and it contained 74 lunar eclipses.
 
==In other fields==
'''Eighty-one''' is also:
*The number of squares on a [[shogi]] playing board
*The year AD '''81''', [[81 BC]], or 1981.
*The number of verses in the Tao Te Ching
*The [[atomic number]] of [[thallium]]
*The symbolic number of the [[Hells Angels]] Motorcycle Club. 'H' and 'A' are the 8th and 1st letter of the alphabet, respectively.<ref>{{citation|title=Despite Outlaw Image, Hells Angels Sue Often|newspaper=[[New York Times]]|first=Serge F.|last=Kovalevski|date=November 28, 2013|url=http://www.nytimes.com/2013/11/29/us/despite-outlaw-image-hells-angels-sue-often.html}}.</ref>
*The title of a [[short film]] by Stephen Burke: ''[[81 (film)|81]]''
*The model number of [[Sinclair ZX81]]
*The number of the [[French department|department in France]] called [[Tarn (department)|Tarn]] [[Image:Tarn-Position.png|thumb|90px|[[Departments of France|Department]] 81 of France ([[Tarn (department)|Tarn]])]]
*The designation of [[Interstate 81]], a freeway that runs from [[Nashville, Tennessee]] to the [[New York]]/Canada border.
*The [[code for international direct dial]] phone calls to [[Japan]]
*One of two [[ISBN]] Group Identifiers for books published in [[India]]
*Number of stanzas or chapters in the [[Tao te Ching]] (in the most common arrangements).
*Number of provinces in [[Turkey]]. 81st one is [[Düzce]].
*Number of prayers said in the Rosary in each night.
*The 81 is a 1965 song by Candy and the Kisses.
*[[Artemis 81]] is a 1981 [[BBC]] TV science fiction drama.
*'The Eighty-One Brothers' is a Japanese fable<ref>http://www.sacred-texts.com/shi/jft2/jft207.htm The Eighty-One Brothers</ref>
 
==In culture==
The Arabic characters for the numerals 8 and 1 are visible in the left palm of the human hand.
In China, 81 always reminds people [[People's Liberation Army]] as it was founded on August 1.
 
== References ==
{{Reflist}}
 
{{Integers|zero}}
 
{{DEFAULTSORT:81 (Number)}}
[[Category:Integers]]

Latest revision as of 07:04, 2 January 2015

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