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 general template is given below to assist in creating and improving these articles.
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?
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. Also, and as importantly in many respects, which cultural and scientific properties (or otherwise) can be attributed to the number? For a complete number article, there need-be at least one accompanying important cultural association aside from mathematical properties present. If you only know one interesting mathematical property, consider jotting it down in an article on a near round number. For instance, if you want to write an article on 1050, see if something about it has already been written on it at 1000. 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 a checklist:
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.
This template (originally developed by Docu) is a subtractive template; i.e. given a number N that has all relevant mathematical properties (even mutually exclusive ones), including extra-mathematical properties. To use this template, replace the in-line generic statements with appropriate information:
N (number)
N (spell out number in bold) is the natural number following N − 1 and preceding N + 1. It is mainly known culturally (or in mathematics) for X and Y reason.
In mathematics
← N − 1 N N + 1 → | |
← x0 x1 x2 x3 x4 N x6 x7 x8 x9 → | |
List of numbers ‧ Integers | |
← y 2y 3y 4y 5y 6y 7y 8y 9y 10y → | |
Cardinal | en |
Ordinal | Nth |
Factorization | 1 × N ( prime) or pa × pb × ... |
Divisors | 1, pa, pb, pc, ..., pa × pb, ..., N |
Roman numeral | "N" |
Binary | "N2" |
... | ... |
Hexadecimal | "N16" |
N is the xth prime number (or composite number), the previous being N − 2y, with which it comprises a twin (or cousin, sexy, ..., for y = 1, 2, 3, ...) prime.
It is also a Mersenne prime, or a Fermat prime, permutable prime, palindromic prime, and so forth; deficient or else abundant, highly composite, etc., if the number is not prime.
It is the sum of n-consecutive primes, px + px+1 + px+2 + ...
N has a Euler totient value of X.
It an X- gonal number.
It is the square of x, or the sum of n consecutive squares.
It occurs in the X- sequence as the nth member, and is an Y- type number.
In normal space, the interior or exterior angles of a X- agon measure N degrees.
In other fields
N is also:
See also
References
For most cases, articles should be named N (number), with the literal spelling of the numbers redirected accordingly (e.g., Four hundred and ninety-six redirects to 496 (number)).
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 1,729 should be 1729 (number), though the article can mention that the number may be written "1,729" or "1.729."
Besides −1, there are no articles on negative integers. Adding information about a negative number therefore can fall under articles representative of numbers' positive, absolute values. One half is the chosen article name for 1⁄2.
It is preferable to have a stub article than to pad an article with trivial or tenuously related information. Normal Wikipedia policies, and guidelines, should be considered when choosing which content to include. Specifically, any scientific and cultural associations of a number, and otherwise, must be verifiable, and covered with due weight.
Remember that the subject of the article is the number — that is, the mathematical object — and not the numeral(s) that represents the string of characters or character commonly used to represent the number. Take care to include only significant extra-mathematical associations of the number that are not trivial.
Do not include content that relates to the article's title only as an identifier, or label, or simple enumeration, or measurement, or as a trivial mention. For example:
If there is plausible ambiguity between such items and the given string of characters, the place to mention it would be on a disambiguation page for the number.
A scientific notion referenced in a number article depends on the mathematics of its properties and characteristics, and how substantial they are, as aforementioned. Examples include:
As well as any other scientific fact that is arithmetically, geometrically, or algebraically tied to the number itself, including by statistical significance, and where equalities near almost integer values.
Highly culturally important references to numbers can be included, such as lucky or unlucky numbers (as a form of numerology), as long as there is a direct reference to mathematical properties of the number, even if mystical (i.e. The One in the philosophy of neoplatonism). See the essay Wikipedia:"In popular culture" content for guidance on how to select appropriate cultural references.
Finally, do not include other general content in the body of the article that is untied to the number as a mathematical object:
Or any notion or item that is not directly relatable to mathematical aspects of the number (in this case, only its numeral is being referenced). If need-be, a hatnote atop the article can be used to link to another article if an important disambiguation is needed. This permits the article to remain focused on information that is primarily number-theoretical.
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 a 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.
It is acceptable for a number article to have few citations if the linked 'word' articles have primary and secondary sourcing.
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 preferable 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!; ¡!, i!; !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 |
Articles for the first twelve integers are some of the most well-developed number articles, in terms of mathematical properties and cultural associations, as well as sourcing. This being said, there are many other number articles that are well-written and can serve as examples:
The following is the status of the project as of January, 2023.
Following the level of priority set by WikiProject Mathematics:
There are four main top-priority mathematics number articles:
Currently, articles for 0 and 1 are well-written within their respective mathematics sections, however they are not generally referenced (even though they contain due links, they could use primary sourcing where possible, even when generalizing). The article for π is a featured article, and the article for e is a good article.
Another fourteen relevant mathematics number articles are categorized as high-priority:
These have all recently been improved (2022-).
At least four relevant mid-priority mathematical article are listed:
Articles that are listed as low-priority include:
Methodical priority assignments to integer number articles have not really taken place, which is something that could be further investigated. For example, 24 (number) could be elevated to mid-priority, given the many important geometric and algebraic properties ligated to it. 12 is another such candidate.
There are continuous individual articles for positive integers from 1 to 299.
Navigation bars inside Docuan tables of number articles have been created with the follow functionality:
Status of disambiguation pages:
For up-to-date and automatically updated list of articles for deletion, see Category:AfD debates subsection 0–9.
If you'd like to be part of the project, simply add your username!
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Some of the following talk pages include it: What links here
To add a message of this project to talk pages of number articles, use Template:NumberTalk that can be displayed with {{WikiProject Numbers}}.
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numbertheory.org – lists of important contributions, number theorists, and concepts of interest