Talk:Aliquot

Mathematics article?
The article is about mathematics, chemistry, pharmaceuticals, music and land surveying. Seems it's a Wiktionary / disambiguation page grown awkwardly. Is this really ok? Shreevatsa (talk) 18:18, 8 April 2009 (UTC)


 * Yeah, I was also wondering whether this shouldn't be turned into a real dab page rather than this half-dab half-article thing it is now. —David Eppstein (talk) 18:37, 8 April 2009 (UTC)


 * I feel the same way. CRGreathouse (t | c) 20:02, 8 April 2009 (UTC)


 * Based on this discussion I went ahead and turned this into a disambiguation page. —David Eppstein (talk) 23:19, 8 April 2009 (UTC)

Egyptian fractions
Interesting, two people that feel the same way about a subject that neither has read in detail. Have either of you read a hieratic text on this topic? To attempt to read/decode ancient Egyptian mathematics, written in ciphered numerals, as Boyer noted in 1944, clear understand of two scribal multiplication methods is required. The first was used by Ahmes outside the text to mentally or otherwise convert rational numbers 2/p and 2/pq to concise unit fraction series by selecting an optimized multiplier (a LCM), 56 in the case of 2/97. In 1895 F. Hultsch was first to report a possible use of aliquot parts in the RMP, a method that E.M. Bruins independently confirmed in 1944. Debates on Ahmes' precise useage of aliquot parts has raged, hot and cold, for over 110 year. After 2002, several Egyptian texts, the most basic was the Egyptian mathematical leather roll outlined the Egyptian method. The most advanced method was presented in the RMP 2/n table.

The second multiplication method was well known to 20the centyr scholars, the duplation method, long proposed to have been Ahmes only multiplication method. This method was primarily used to establish proofs, likely following an Old Kingdom tradition. For example, RMP 38 proved that 35/11 times 320 (ro a volume unit) was also multiplied by 1/10, making the calculation 320 x 7/22, obtaining 101 9/11 (let's skip the unit fraction conversion step to make a point). Ahmes' proof contained a second side, also written in duplation multiplication, returning the starting 320 value. 101 9/11 was multiplied by 22/7, obtaining the correct 320. Q.E.D. (for Ahmes and myself).

Best Regards, Milogardner (talk)Milo Gardner 4/8/09 3:51 PST


 * We don't need you to describe Egyptian mathematics here on the talk page. What is needed is an explanation of why someone looking up the word "aliquot" would want to be presented with this material, which on the face of it has little or nothing to do with the word. —David Eppstein (talk) 23:00, 8 April 2009 (UTC)


 * I don't read Ancient Egyptian (not hieratic, hieroglyphic, or even demotic) so I'd have to say "no" to your query. I have, however, studied Ahmes' papyrus and am familiar with Egyptian numerals, Egyptian fractions, their multiplication method, and certain scribal conventions (how to "reduce" fractions, etc.).  But I don't see how that relates to this article!
 * CRGreathouse (t | c) 01:15, 9 April 2009 (UTC)

To directly answer David's question, Oystein Ore's book "Number Theory and its History", available by Dover reprints, dedicates a chapter to aliquot parts on (pages 86 to 115) in which perfect numbers, LCMs, GCD's, Greeks, Arabs and medieval arithmetic/number theory is discussed. Today, scholars do not have full access to Greek mathematical texts, outside of Arab, Byzantine, and medieval 'copies' in sufficient quantity to fairly parse Greek arithmetic and number theory uses of aliquot parts. However, Egyptian texts do exist in sufficient quantity. For example, RMP 79 presents a recreational problem that Ore cites on page 116-118 as being copied phrase by phrase by medieval poets -- presenting a riddle -- stripping away Egyptian fractions, its useage of aliquot parts, LCMs as scaling multipliers, exposes Egyptian rational number arithmetic operations to be almost identical to our own, Hence, as Egyptians, Greeks, Arabs and medievals thought of aliquots, so did Fermat and those in our European history of number theory. Need I document additional threads that link 4,000 years of proto-number theory to our modern number theory, using Ore's book as a bridge? best regards, Milogardner (talk)milogardner, 4/9/09, 8:50 AM, PST.


 * Let's try asking this another way. This article is now a disambiguation page. It only gives brief listings to other articles that people might think "aliquot" should refer to. So, one of the listings is already to aliquot part. Is there another phrase "aliquot X" that should also be listed and isn't? Is there any important difference in meaning between "aliquot part" as used by modern mathematicians and as used by modern historians of mathematics? Or are we done here? —David Eppstein (talk) 16:09, 9 April 2009 (UTC)

Non-standard DAB
This is a reply to David Eppstein's comment on my talk page about reverting my changes.

This page suffers from a number of problems, IMHO.
 * The introductory line is way too long—look at the examples in WP:MOSDAB. It should not contain any etymology, that's what the Wiktionary link is for.  Please read this guideline which explains that disambiguation pages are not to contain dictionary definitions.  It doesn't matter that the Wiktionary entry is sub-par, that's their problem.
 * Individual entries are also far too long. You should read all of WP:MOSDAB carefully, but especially this section.  The entries on this page break almost every style guideline there:
 * Entries should nearly always be sentence fragments
 * Each entry should have exactly one navigable (blue) link
 * The description associated with a link should be kept to a minimum, just sufficient to allow the reader to find the correct link
 * The (totally non-standard) "Additionally" section contains entries which do not correspond to any article at all. Two of the articles these entries point to do not even mention the term aliquot!

This last point, I think, is a good example of the most common mis-understanding about what a disambiguation page is. It is not a list of meanings of the term in question. It is a list of articles that the user might conceivably have been looking for when they typed in an ambiguous term, as the first sentence of Disambiguation makes clear. No one is going to type in "aliquot" to try to find the chemistry page, thus there should be no such entry especially since chemistry doesn't say anything at all about the term. We might argue about the very last entry, since the PLSS article at least mentions the term.

In short, the ideal version of this page according to WP:MOSDAB is far closer to the version you reverted than the current state. I'll make these changes one at a time, if you prefer, with pointers to the appropriate sections of the guidelines. —johndburger 03:33, 7 April 2011 (UTC)
 * Part of the issue is that this used to be a (bad) article before it was converted to a dab. I agree that the extra blue link in one line should go. And we can get rid of the word "is" in most of the entries if writing in fragments makes you happier. But I think the length of each entry (a single line, but with enough detail to clearly describe the meanings and allow them to be distinguished from each other) is about rigt. And the "additionally" section contains meanings which are used in several mainspace articles including several that bluelink to this dab page, so I think removing those entries would be a big mistake. And in particular, the two very different meanings of "aliquot part" need disambiguation, despite the fact that only one of them is a bluelink. The only thing that seems to be nonstandard about the "Additionally" section is that it is not headed "Aliquot may also refer to:" as the example in MOS:DAB suggests. —David Eppstein (talk) 04:22, 7 April 2011 (UTC)