Talk:Regular number

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Mathematics rating: B Class Mid Priority  Field: Number theory (historical)
Articles for deletion This article was nominated for deletion on 7 July 2006. The result of the discussion was delete.

This is a new, sourced, write-up of the reference to this term I happen to know. Eric Weisstein has inserted a a note in MathWorld about a (slightly different) generalization of the term, and the article on that was deleted, perhaps rightly. Septentrionalis 21:10, 13 July 2006 (UTC)

This seems fine, except that I'd wager there are other uses of the term out in the literature somewhere. I'm not quite bored enough to go looking for them right now, but if someone else is, maybe he'd like to make a disambiguation page. --Trovatore 18:53, 30 July 2006 (UTC)
I have better sourced and significantly expanded this article, and merged from Hamming number some additional content. I didn't include a link to MathWorld because that describes a different concept ({2,5}-smooth as opposed to {2,3,5}-smooth numbers) on which there seems less scholarly work. —David Eppstein 06:51, 13 March 2007 (UTC)

[edit] Name

I don't think that Regular number is a good location for this article. I haven't ever seen that term used to mean a 5-smooth integer, although I have seen it used once or twice with other meanings. Further, the term Hamming number is used fairly widely. Although they will always be "5-smooth" to me (or perhaps {2, 3, 5}-smooth), I think that Hamming number is the right place for this article. Thoughts?

CRGreathouse (t | c) 21:09, 2 March 2008 (UTC)

"Regular number" is the term used in the context of Babylonian studies; see the titles of several of the references. Similarly, Hamming number is the term used in the context of functional programming. Both names seem somewhat specialized, as does the awkward "{2,3,5}-smooth number". But as long as we don't go for the "ugly number" name, I don't really have a strong opinion on which should be primary. I suppose "Hamming number" would fit with the longstanding mathematical tradition of naming things after latecomers to the study of those things (Hamming wasn't even the first to talk about algorithms for computing these numbers, he was merely the first to talk about generating them in order). —David Eppstein (talk) 21:13, 2 March 2008 (UTC)
Of course if we were to find the name of the Babylonian who first classified these numbers I'd be happy to name the page after her/him. :) CRGreathouse (t | c) 22:52, 2 March 2008 (UTC)
http://mathworld.wolfram.com/RegularNumber.html says: "A regular number, also called a finite decimal (Havil 2003, p. 25), is a positive number that has a finite decimal expansion." http://www.britannica.com/eb/topic-496213/regular-number says: "Regular numbers are those whose prime factors divide the base; the reciprocals of such numbers thus have only a finite number of places (by contrast, the reciprocals of nonregular numbers produce an infinitely repeating numeral). In base 10, for example, only numbers with factors of 2 and 5". The Babylonians used base 60 so a Babylonian regular number is consistent with the Britannica definition. MathWorld is about the reciprocal and assumes base 10, so no factor 3 allowed. How about splitting the article? Regular number could use the Britannica definition but also mention other definitions. Hamming number would only be about 5-smooth numbers. Babylonian mathematics and everything base-related could stay in Regular number, and base-independent 5-smooth things could move to Hamming number. PrimeHunter (talk) 02:12, 3 March 2008 (UTC)
I think much of the value of the article has to do with bringing together the different names people have used in very different subject areas for the same concept. Splitting it would lose that. The MathWorld decimal definition already went through an AfD and was deleted. And much of the content here looks specific to base 60. But if you can find sufficient sources to support an article on the general concept of regularity in any base, I don't see any reason to object to having the "regular number" title point to that article and having this article under a different title, with cross-links between the two. —David Eppstein (talk) 02:22, 3 March 2008 (UTC)
I didn't know Wikipedia:Articles for deletion/Regular number. It's probably best to keep the article in one place, maybe with a brief mention that other definitions exist. PrimeHunter (talk) 03:14, 3 March 2008 (UTC)

[edit] "Ugly" numbers?

Should Wikipedia record (and mention in such a prominent place as the opening paragraph of the article) a nonce term apparently made up and only ever used in the context of some forgotten computing contest? And may I ask what reason was given for such a label by whoever coined it? The term "ugly number" strikes me as terribly POV, and moreover its strong pejorative character seems completely ludicrous and unwarranted given the high notability and usefulness of these numbers for all kinds of purposes (starting by their utmost importance in geometry and music). It seems as if whoever thought such a dismissive label as "ugly" was somehow befitting for these numbers, must have thought that "number beauty" is measured by arcanity and lack of pragmatic value, so that the quantities that govern myriad aspects of our daily lives would appear "ugly" because they are to be found all around. 213.37.6.23 (talk) 09:57, 8 May 2008 (UTC)

Agreed. Removed. SethTisue (talk) 11:28, 9 May 2008 (UTC)

[edit] Algorithms for computing regular sexagesimals in order

I expanded a previous footnote into a paragraph about computing sexagesimals in order, after discovering the Knuth and Bruins references on the subject as well as the Gingerich citation we already had. I'd also like to add something like "Eppstein (2007) describes an algorithm for computing tables of this type in linear time for arbitrary values of k.", with a later bibliography entry Eppstein, David (2007), The range-restricted Hamming problem, <http://11011110.livejournal.com/95519.html> . But as you can see, that would be a little self-serving. If someone else thinks this would be an appropriate addition, please go ahead and add it. —David Eppstein (talk) 18:22, 27 May 2008 (UTC)