Wikipedia:WikiProject Numbers

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This WikiProject is aimed at standardizing the pages on numbers. Although most of the articles on numbers currently follow a format, they do so to varying degrees. A template is given below based on the general tendencies of the number articles so far. Once the template has been examined and optimized, then the work will begin of converting each number article to conform.

Contents

[edit] Flagship number article

The article on the number 12 has been chosen to be the article representative of this WikiProject.

[edit] How far to go?

See also Wikipedia:Notability (numbers).

There is no need to remind anyone here that there are infinitely many numbers, for we all already know that. Despite what some may rant, no one here has any intention of making a robot to make number articles. All number articles will be written by humans, because we want to have articles on numbers that humans might want to look up; thus the articles will take into account the humanistic qualities of numbers.

So the question is, what numbers should there be articles for? These are proposals:

  • Integers: Continuous from −1 to 200. Multiples of 100 from 300 to 900, then multiples of 1000 to 9000. Afterwards, only powers of 10 (from 1 up to 1011, higher than that only if they have a standard word name and commonly used SI prefix) and numbers with some remarkable mathematical property.
  • Fractions: Definitely 1/2, possibly 2/3 and 3/5, fractions that are in common use and have a code point assigned in the Unicode Number Forms block. (Composed characters don't count).
  • Reals: Important mathematical constants such as e and π.
  • Imaginaries: At the very least, i
  • Non-numerical entities: NaN, with a possible redirect from Not a Number
  • Number bases: Those that are actually used (or have been used in the past) for practical calculations, such as binary, octal, decimal, hexadecimal and sexagesimal.

[edit] Template for integers

[edit] Outline of template

Each article on a number ought to consist of two major sections, the first dealing with the mathematical properties of the number, the second dealing with the extramathematical properties of the number, such as cultural associations of the number.

  1. Mathematical properties
    1. Representation (decimal, Roman, Mayan, hexadecimal, etc.)
    2. Arithmetic, number theory properties
    3. Algebraic properties
    4. Calculus properties
    5. Geometric properties
  2. Extramathematical properties
    1. Most universal and eternal
    2. Most local and ephemeral still worth listing.

[edit] Template proposals for integers

User:Docu has come up with a very nice format he used on 37, and this format is now the favored proposal for a template. This template has been developed into a substractive template; i.e. given a fictitious Number N that has all mathematical properties (even mutually exclusive ones) and all kinds of extramathematical properties, this template shows them all. Someone using the developed template will take it, delete the statements not applicable to the number in question, then fill in the appropriate values.

Number N (Digit 10's place of Number N-Digit 1's place of Number N) is the natural number following N - 1 and preceeding N + 1.

Number N
Cardinal N
Ordinal Nth
Numeral system N-cimal or N-ary
Factorization (prime number) or px ... py
Roman numeral N
Binary N2
Hexadecimal N16

[edit] Mathematics

It is a prime number, a Mersenne prime, a Fermat prime, a permutable prime, a palindromic prime, a composite number, a highly composite number, an abundant number, a surreal number, and an amicable number with 0.

Note that these should be links to the relevant articles (which already contain lists of that kind of number). There's little point in creating, say, a category of Mersenne primes; especially since most Mersenne primes won't ever have their own article.

[edit] Other fields

Thirty-seven is:

[edit] External link

The previous template proposal merely codified and organized the tendencies already evident in the existing number articles. This proposal required less work (merely uniformizing). The only problem with it is that it doesn't fall into line with the format generally used for WikiProject articles. Here is that old proposal, used on our fictitious Number N.

(* Mathematical properties section *)

Number N is the natural number following Number N - 1 and preceding Number N + 1. It is the Xth prime number, the previous being Number N - 2x, with which it comprises a twin prime, the next being Number N + 2x, with which it comprises a twin prime. It is also a Mersenne prime, a Fermat prime, a factorial prime, a primorial prime, a permutable prime, and a palindromic prime. It is a composite number, with its divisors being d1 ... dx, making it a highly composite number and its factorization

N = px ... pz

makes it a sphenic number.

It is the sum of three consecutive primes, (px + px+1 + px+2), the sum of four consecutive primes (px + px+1 + px+2 + px+3), and the sum of five consecutive primes (px + px+1 + px+2 + px+3 + px+4).

It a triangular number and the square of x. It occurs in the Fibonacci sequence and is a Lucas number. It is a Catalan number. It is the magic result of an x by x magic square.

In normal space, the interior or exterior angles of a X-agon measure Number N degrees each.

Number N is also

  • The atomic number of elementium.
  • The atomic number of an element temporarily called LatinNumberium. (* If the element has not even been discovered, it should not even be mentioned. *)
  • The Messier Number of Object A
  • The NGC (New General Catalog) Number of Object A
  • The Saros Number of a solar (or lunar) eclipse series.
  • Considered lucky in Country A.
  • Considered unlucky in Country B.
  • Very important in Religion A's sacred texts. (* Better to let Wikipedians versed in theology decide which religious associations of a number ought to be included *)
  • The designation of Country A's Highway Route Number N, which runs from Point A to Point B. (* Only major highways need be included, unless they have achieved fame beyond their location. *)
  • The code for international direct dial phone calls to Country A.
  • The registry number of the USS/HMS/RMS ShipName, CVN-Number N. (* Only major ships, such as aircraft carriers and gigantic cruise liners need be included *)
  • In the expression "folksy expression with Number N".
  • In the title of the movie There's Something About Number N. (* Only major studio releases ought to be included. Include independent releases if they achieve fame comparable to a major studio release. *)
  • In sport, the retired jersey number of legendary player Babe McGwire.

[edit] Criterion for including cultural associations

In spite of the stub-like bareness of some of the number articles, some worry that all number articles could become overrun with trivial information. Therefore, a criterion is needed for determining if something is worth including. One proposed criterion is if the cultural association is held by a significantly large group of people. For example, if Joe Schmuck is the only person on Earth who considers 154 to be unlucky, then it's not worth including in the article on 154. But if the entire state of Wisconsin thinks 154 is unlucky, then it should be included in the article on 154.

[edit] Numbers in religion

In general, only numbers mentioned in the religion's sacred texts are worth mentioning in the number articles.

Roman Catholic dogma holds that all passages of the Bible are equally inspired. Therefore, any number in the text of the Bible given with precision is worth mentioning in the appropriate number article. Be sure to cite book, chapter and verse. Numbers that depend on a particular edition, such as page numbers or footnote numbers are generally not considered important.

[edit] Numbers in numerology

In modern Western numerology, the names and birthday of a person are reduced to a single digit using modular arithmetic. The 2-digit numbers 11 and 22 have special significance, but any other number besides 0 through 9 is not important to numerological divination. It might be acceptable to make an insert in the articles for 0 through 9 about their numerological significance.

It's important not to confuse numerology (a pseudoscience) with recreational mathematics, superstition, coincidences, etc. E.g., 13 is considered unlucky by many, but in numerology, 13 is nothing more than a 4. The fact that the palindromic prime 10^11310 + 4661664 x 105652 + 1 has 11311 digits (one more than the exponent of 10 in the expression) is a coincidence in base 10, and could be labelled "recreational mathematics" without being considered pejorative. To label it "numerology" (which it clearly is not) could be considered offensive.

[edit] Numbers in fiction

In general, the number needs to be conspicuous and important to the story to be worth mentioning in the number articles. Appearing in the title is often a guarantee of conspicuousness and importance.

[edit] Numbers of Pokémon

Each Pokémon has a number associated in the trading cards games and video games. These numbers are not used in the TV shows or movies. There was some sense of logic and order in the original set of 150, for example, Pikachu, #25, evolves to Raichu, #26. But with the addition of newer Pokémon, some of which evolve from or to Pokémon in the original set, order is no longer important. For example, Pichu, #172, evolves to Pikachu, #25, giving the sequence 172 25 26. There is nothing particularly "25" about Pikachu any more than there is anything particularly "172" about Pichu.

Therefore, numbers of Pokémon are not considered important enough to list in articles about numbers, other than total numbers of Pokémon, such as 150 total in the original set.

[edit] Numbers in Star Trek

Lots of numbers occur im passim in Star Trek. It is safe to say that any integer from 1 to 99 has occurred at least twice in some episode of Star Trek, and that any integer from 100 to 999 has occurred at least once, if only as a substring. To merit mention in an article about a number, the number must be an important part of the mythology of Star Trek, such as 1701.

47. The high incidence of the number 47 in Star Trek is noted on the page on 47, which also provides a link to a list of references to 47 at Memory Alpha, a Star Trek wiki.

[edit] Numbers in sports

Numbers that appear in the official rules of the game, such as the total number of players per team, number of game partitions (e.g., 9 innings in baseball) are worth mentioning in the number articles.

A record is worth mentioning if it is from a Major League player, or if it appears in the Guinness Book of World Records. Be sure to indicate the year the record was set in order to facilitate removal when a new record is set.

In sports where the number on a player's shirt is not determined by the position he plays, only numbers that have been retired by a Major League team are worth noting. But if a player's number is determined by the position he plays, this probably falls under the rules of the game consideration above.

[edit] NASCAR numbers

Car numbers of teams that have won the Daytona 500 or the NEXTEL Cup Series championship are worth noting in the articles on the corresponding numbers.

[edit] Numbers in currency

Note: unless a country is specified, the term "dollar" will be used here as a generic unit of currency equal to 100 cents.

Some numbers are very commonly used as denominations of dollars and/or cents (e.g., 1, 5, 10, 100). Some denominations are official but fail to gain public acceptance (e.g., the US$.50 coin, the US$2 bill). Some facetious usages may be worth noting (e.g., the $3 bill). But the vast majority of integers are never used as official denominations (e.g., 8, 47, 1729, etc.) Therefore, it is worth noting if a particular number is commonly used as a denomination of dollar in many countries of the world.

Currency conversion values should not be included in the number articles. Those values fluctuate on a daily basis and are often floating point values. One possible exception to this might be when there is a historic concerted effort to bring a conversion value to a certain target value. For example, when Japan tried to make 100円 = US$1.

[edit] Numbers in statistics

For the statistical significance of a number to be worth including in a number article, it must either be:

  1. A number of axiomatic importance to the principles of statistics, i.e., a number that appears in many of the formulas used by statisticians. That's probably numbers like 1, 2 and π.
  2. A statistic that has attained historical or mythical status. "One half of all marriages end in divorce" is one example.

The goal is not to crowd number articles with raw statistical data where the explicit numbers change depending on the way the statistic is worded. For example, every minute, 17 people die of a certain disease. That would be 1020 dead every hour, 24480 every day, 8935200 every year (8959680 on leap years), etc.

Also, statistics that are in progress should not be included. As of this writing, over 1000 American servicemembers have died in Iraq. Sadly, that number will probably reach 2000. Although this number is important to us as human beings, it is of no concern to this project until the exact number is finalized.

[edit] Numbers in McDonald's Monopoly game

Each McDonald's Monopoly game piece has two numbers on it. One is a 10-digit base 36 number that appears to be unique to each individual game piece (and therefore definitely not worth listing here on Wikipedia). The other is a 4-digit base 10 number, with the first two places telling what iteration of the game the game piece is for, and the other relates to its location on the board. For example, a fourth iteration North Carolina Avenue game piece has the number 4019 on it. But since the name and color of the game piece is more strongly associated in the player's mind, the numbers are at this time not considered worth listing in Wikipedia. For the curious, however, User:PrimeFan has listed the location numbers on his user page.

[edit] Citations

Just as with any information in Wikipedia, articles on numbers need to cite sources. (See Wikipedia:Citing sources for general information on citing sources).

Some statements that are easily verified with a pocket calculator might not need citations (e.g., the fact that 73 = 343), but anything slightly more difficult to verify does (e.g., that 786 might be the largest number for which 2nCn is not divisible by the square of an odd prime).

It is not the place of this project to prescribe a citation format. Until Wikipedia decides on an uniform citation format, number articles may use whatever citation format would be acceptable in a mathematics journal

The OEIS and Mathworld are respectable Web sources, as are Web versions of respected professional journals.

For now (June 2006), it is acceptable for a number article not to have citations if all the linked 'word' articles do.

[edit] Article naming and number nomenclature

The issue of naming number articles went through a vote. User:Egil's proposal for naming the articles Number N (number), and making the spelled out names of the numbers be redirects, (e.g, Four hundred and ninety-six redirects to 496 (number)), received the most votes, and with the initiative of User:Dysprosia, the articles were moved accordingly. The issue of whether the "British" spelling out of numbers or the "American" spelling out should be used remains, but is no longer as pressing as it once was.

Numbers deserving their own article that are greater than 999, should have the article title written in digits without any separators between the digits of the integer part. Writing the number with separators may of course be acknowledged in the body of the article. Thus, the article on the taxicab number should be 1729 (number), though the article can mention that the number may be written "1,729" or "1.729."

[edit] Growers

For numbers from 120 to 199, "growers" should be made in which numbers are grouped in tens, containing very short stubs for each number. When it is judged that the article for a particular number is big enough, it is made into its own article. For number from 200 to 999, growers might be groups of hundreds, containing extremely short stubs for each number. Beyond about 1024, there might not be much to say about each number. But if an article is written on a non-round number beyond 1000, then a link to it should be added in the nearest lowest round number for which there is an article.

[edit] Alternative to creating articles on negative integers

User:PrimeFan doesn't think it necessary to write articles on negative integers besides -1, but he wouldn't mind being proven wrong. An alternative, for now, however, is to make additions to the article on the absolute value of the negative number in question.

[edit] Before creating a new article

Even if a number is within the range given above, care should be taken to only create a new article on a number if there is sufficient known information to create an article that consists of more than just "N comes after N - 1 and before N + 1". As a guideline, you ought to know at least three interesting properties of a number. What constitutes interesting can be debated (see Wikipedia:Evaluating how interesting an integer's mathematical property is for one possible way of gauging this), but the point is that the careless creation of number article stubs is to be avoided.

If you only know one interesting property, consider jotting it down in an article on a near round number. For instance, if you want to write an article on 10123, see if something about it has already been written on it at 10000. That's the point of the series of stubs at the ends of articles like 500 and 7000, to see if there are numbers outside the declared project range that might merit their own article.

So before creating a new article on a number, go over this checklist:

  1. See if something about the number has already been written about the number at an article on a near round number (rounding down).
  2. Name at least three interesting and unrelated properties of the number (or one earth-shatteringly interesting property, such as odd perfect number, or a quasiperfect number of either parity).
  3. Fill out a Docuan table with the basic properties of the number (factorization, binary representation, etc.)

[edit] Edit summaries

Every project member (indeed anyone who edits Wikipedia) is encouraged to write brief but complete edit summaries. (See Wikipedia:Edit summary for advice on writing edit summaries for articles on any topic).

For articles about numbers, or mathematics in general, it is advisable to use "linear algebra" (algebra typeset into a single line, without superscripts or subscripts) or pseudocode.

For example, instead of writing "Corrected mathematical formula to sum of reciprocals of squares of factorials instead of sum of reciprocals of factorials of squares, corrected links to Italian, Chinese Wikipedias", you could write "Corrected formula Sum(1/n!^2) instead of Sum(1/n^2!), corrected it:, zh:"

In edit summaries, use the mathematical operators available on the standard keyboard (+, -, *, /, ^) even though a different operator (e.g., ×) would be more appropriate in the article text.

Although Greek letters can technically be used in edit summaries, it is preferrable to use the name of the letter spelled out in the English alphabet. For example, "Changed e to pi in formula", "Mu(100) is 0, not 1" (The article text should of course fully avail itself to any applicable Greek letters).

Some shorthand notations that might be useful:

n, num, # An arbitrary integer
p An arbitrary prime number
x, num, # An arbitrary real number
val Value
tri; sq, ^2; pentag; hexag; heptag, etc. Triangular; square; pentagonal; hexagonal; heptagonal, etc.
sum; prod Sum; product
!; !!; super!, $!; hyper!; ¡!; !sum; 1/! Factorial; double factorial; superfactorial; hyperfactorial; alternating factorial; factorial sum; reciprocal of factorial
bin; oct; dec; hex Binary; octal; decimal; hexadecimal
Infobox, Docuan table The table with binary, hexadecimal representation, factorization and other general data points about the number

[edit] Participating Wikipedians

[edit] Signed up

[edit] To be asked to sign up

These members have already done great work on number articles. Asking them to sign up is more than a formality, however. It is to better coordinate the project.

User:GUllman

[edit] Progress report

The following is the status of the project as of May 15, 2004. (This should be updated at least once monthly until project is complete).

[edit] Creation of articles

There are continuous individual articles for positive integers from 1 to 120. Then from 120 to 190 they skip by tens, including very short stubs for non-round numbers in the range 121 to 199, (though a few have their own articles, such as 121, 137, 153 and 169.

From 200 to 900 they skip by hundreds, including very short stubs for some numbers in the range 201 to 999 (mostly a list of one-liners only including numbers that have any info at all), though again a few numbers have separate articles, such as 220, 284, 360 666 and 720.

From one thousand to 9000, they skip by thousands, following the same scheme used for the groups of hundreds; again, some (1001 and 1729 spring to mind) have their own articles. 10000 covers all five-digit numbers. +sj+

Navigation bars have been created for 0-9, 10-19, ..., 110-119, and for 100-190 by tens, for 200-900 by hundreds, and for 1k-9k by thousands. +sj+

-1, 0, and the fraction 1/2 has its own article.

[edit] Naming compliance

Thanks to User:Dysprosia's initiative, most of the number articles, from 1 to 1001 have been moved according to the naming vote. Negative one and One half have not yet been moved, and there might be a few others still remaining to be moved. After that task is complete, it will be nice (but not urgent) to look at the "What links here" page on each number article and change the links accordingly. User:PrimeFan volunteered for this task, and decided to start with the links to 47 (number). His plan is to do one number a day. He will not touch links from other Users' pages or from Talk pages, though.

[edit] Content formatting compliance

The numbers -1 through 121, and all the larger numbers that have their own article, have data tables (also known as "Docuan tables", named after the User who came up with the format) per the template. Rejoice!

[edit] Articles listed at Articles for deletion

[edit] Current

[edit] Kept

[edit] Deleted

[edit] Redirected

[edit] Message for talk pages

There is a message that can be added to the talk pages, Template:NumberTalk, it can be displayed with {{NumberTalk}}. Currently it displays the following:

This article is part of WikiProject Numbers, an attempt at creating a standardized, informative and easy-to-use resource about numbers. Suggestions for improving multiple articles on numbers and related subjects should go to Wikipedia talk:WikiProject Numbers.


Some of the following talk pages include it: What links here

[edit] Report on international cooperation

Wikipedians working on Wikipedias in other languages have realized the tremendous informative value of articles on individual numbers and have begun to create their own versions of the List of numbers and of individual number articles. The Japanese Wikipedia was far ahead of the pack, however, with articles on all the integers 1 to 100 before the English Wikipedia attained that landmark.

As of 15 May 2004, The Spanish Wikipedia has achieved that goal with 100% of the first 100, with the equivalent WikiProject being spearheaded by User:Sabbut in a format with a colorful predecessor to the Docuan table, sometimes referred to as "tabla de Sabbut". Content formatting compliance is estimated to be approximately 80%.

The Italian Wikipedia went in about three months gone from 0% to 93%, by copying and translating number articles from the Spanish Wikipedia. Sometime before September 2004, it reached 100%. The latest edits consist of adding categories.

The Swedish Wikipedia was making slow but steady progress, basing most of the articles on an old format User:Docu used for the English pages on 80 - 89, but after a quick burst of activity from Användare:Mike, the Swedish Wikipedia has reached 100%.

The Slovenian Wikipedia has started making progress in April 2004, and now, February 7, 2005, it stands at 97% of the first 100 integers, plus a few important transcendental numbers such as π and e. User:Anton Mravcek chose 12 as the starting point, in a spartan format with a Docuan table. User:XJamRastafire refined the format, and added to the Docuan table a splash of color and fields for the Euler totient function, divisor function, divisor sum, prime-counting function, Möbius and Mertens functions. This is sometimes called the Sabbutsdokujeva škatla in edit summaries.

Slord thought up of starting this project on the French Wikipedia, making a Liste de nombres page. But that page stood with its links to the numbers 1 to 100 in red for a long time, until other users decided to simplify the page. But the older format was restored, and as of February 2005, the French Wikipedia has not only achieved 100% of the first 100 integers, but also has an article on each number from 101 to 199 (something towards which the English Wikipedia has hesitated).

The German Wikipedia has articles on 16% of the first 100, with remarks on the others in the list of numbers.

As of December 2004, the Portuguese Wikipedia stands at 45%, consisting of the numbers in order from 1 to 45. The Hebrew Wikipedia has an article on 42, but no other number as far as I can tell.

On 8 April 2004, User:PrimeFan noticed that User:Glenn has been adding interwiki links to articles on numbers in the Nahuatl language Wikipedia.

On 18 May 2004, Yozh created an article on 43 in the Russian Wikipedia and a List of prime numbers. There doesn't appear to be a List of numbers.

On 1 June 2004, PrimeFan noticed that all the number articles in the Spanish and Italian Wikipedias are messed up. Seems to have something do with the Wikipedia surface redesign interfering with the parsing of the Sabbutian tables.

On 4 February 2005, User:Gebruiker:Dedalus in the Netherlands noticed that in de Dutch (nl:) Wikipedia the list on numbers has reached 23, with the last just being a stub. I worked the last week to include (stub) articles for the numbers 15 to 23, and edited quit a lot in 0 to 14, uniformizing the articles and including Docuan tables. Speaking on Docuan tables, in the english page on 9 (number) the Docuan table included a lot of rows with references to a lot of ways of writing the digit in other languages. The digits 0 to 8 are still lacking these references however. I included references to other languages in most of the digits, however probably messing with the unicode representation of Chinese and Japanese digits (or, the Unicode reference to digits is not in a contiguous block). nl:Gebruiker:Dedalus also noticed that on the German Wikipedia a fanatic deletionist is busy removing most of the articles on individual small integers, while on the Dutch Wikipedia these articles are included in the hundred most wanted by Andre Engels.

[edit] Lists of numbers

[edit] See also

v • d • e
Number systems
Other