Talk:Egyptian fraction

Hmm, interesting changes made by Paul G. I could be wrong, but I think the "sum of distinct unit fractions" sense is the much more widely used. And I think it was appropriate to put it in number theory category. See the wikipedia entry w:Egyptian fraction, where the "single unit fraction" sense isn't even mentioned, but where the connections with number theory are expounded upon at great lengths. There are number theorists today who are actively studying Egyptian fractions. By contrast, Egyptian fractions have been pretty much useless as an arithmetic device since, well, since ancient Egypt :-) I'll wait and see if anyone offers any contrary discussion before changing things back... :-)

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Egyptian fraction

(moved)

--Connel MacKenzie 19:32, 24 February 2007 (UTC)

I'd have to search hard to find good citations, but this is a real computational method attributed to Egyptian mathematicians. I can't say whether the name of the method is consistent, though. This looks more like part of a Wikipedia article; all we need is the term unit fraction for a fraction with a numerator of 1. --EncycloPetey 19:39, 24 February 2007 (UTC)

Thank you very much Connel MacKenzie for rfv'ing this, because in researching it, I found that there's actually another sense used by some authors which I was not aware of. I'll add that to the entry. Thanks a ton, thanks to you I have learned a little more about my world!!! :D Anyway, the following books witness that the word is a great addition to Wiktionary.

1997: "Numbers and geometry", p. 3. John Stillwell. As another example, an Egyptian fraction for ${\frac {3}{5}}$ is ${\frac {1}{2}}+{\frac {1}{10}}$. (emphasis mine)

2000: "Mathematica in Action", p. 322. Stan. Wagon. Thus we will use the term Egyptian fraction to refer to a representation as a sum of distinct unit fractions. (emphasis theirs)

(Date not known by b.g.c): "Kendall/Hunt Pre-algebra Teacher Guide", p. 80. (Author not known by b.g.c) Challenge a classmate to an Egyptian fraction duel. (emphasis mine)

2006: "Real Infinite Series", p. 81. Daniel D. Bonar, Michael J Khoury. Express 2/5 as a finite selective sum of the harmonic series (i.e., as an Egyptian fraction). (emphasis mine)

—This unsigned comment was added by Language Lover (talk • contribs).

Mathematical vocabulary is something I have spent a lot of time studying. One of my mathematics dictionaries gives:

• "a fraction of the form 1/n" (Dictionary of Mathematics, Borowski and Borwein, Collins, 1989); this is generally a reliable resource)

Interestingly, I don't find it in either of my other mathematics dictionaries, nor in the OED (second edition), nor in Chambers, but definitely exists. A couple of points, though:

• As EncycloPetey hints at, "unit fraction" is probably the more commonly used term among mathematicians (and is more understandable); "Egyptian fraction" probably appeals more to schoolchildren learning fractions.
• The Egyptians used only unit fractions and 2/3, but the term "Egyptian fraction" does not include 2/3. — Paul G 08:08, 25 February 2007 (UTC)

Wow, this is very interesting. I've never looked in "math dictionaries" (and only had a vague notion that such things even existed)... most my math lexicon comes from lectures and textbooks (I'm a math doctoral student). I find it very interesting to see how much dispute there is over something I thought was pretty much agreed on. Well, I could be wrong, but I think Borowski and Collins aren't giving the full sense (they can be forgiven, of course, since their dictionary was written over 15 years ago). See w:Egyptian fraction (which, btw, I had no hand in writing), which doesn't mention the "unit fraction" synonym sense at all (and which, incidentally, contains copious links and references dispelling any ghost of a thought that this word isn't proper English)  :-)

unit fraction would not be a synonym of Egyptian fraction. An Egyptian fraction would be a sum of unit fractions. At least, all the sources I've seen so far use it that way, if they use it at all. --EncycloPetey 04:29, 26 February 2007 (UTC)

It looks like there are two definitions in existence. One is indeed a synonym of "unit fraction", and the other is a sum of unit fractions. — Paul G 12:54, 4 March 2007 (UTC)

Hm, I'm coming to doubt my own beliefs now. Wikipedia has only the "sum of unit fractions" sense, while my maths dictionary has only the "unit fraction" sense. I've asked about it over at Wikipedia as no doubt they have done more research there than we have. — Paul G 13:04, 4 March 2007 (UTC)

Wikipedia asked me to give my references. I have only one — the one I have given here. They have a stack of references with the "sum of unit fractions" sense, and so does the Mathworld article. See my response on the Wikipedia discussion page. It looks like my reference is probably wrong, in the absence of any other references. The authors don't say where they got their definition from - it could just be that's what they thought it meant and that they didn't bother to check.

My copy of Borowski and Borwein is the first edition. Does anyone have a later edition (either of their own, or that they could look at in a bookshop or library) that they could check to see if the definition has been updated? — Paul G 18:02, 14 March 2007 (UTC)

A books.google.com search does show some authors using your sense. Which surprised me when I saw it :-) I absolutely love the quirks of English!! :D So don't feel bad, your sense seems to also be attested, just much less frequently. Thanks for all the work you've been doing for this entry, you are truly a great wiktionary contributor :-) Signed, Language Lover

RFV extended from February. — Beobach972 20:49, 3 June 2007 (UTC)

Looks like "rfvpassed" to me, by "Appearance in a refereed academic journal" but I've been surprised before. --Connel MacKenzie 15:58, 5 June 2007 (UTC)

Definitely passed. Not a sum of parts and no shortage of references.

• or select from 60+ other books

If somebody wants to take care of undeleting narf, I'll be happy to fill in the reference section for EF.--Halliburton Shill 03:02, 7 June 2007 (UTC)

Struck. RFV passed. bd2412 T 03:04, 10 November 2007 (UTC)

Simplest form?

Didn't the Egyptians normally use the simplest sum of unit fractions (e.g. three quarters = a half plus a quarter), not an unnecessarily complicated form such as that used as an example in the definition? Dbfirs 21:22, 17 September 2008 (UTC)

Actually, the Wikipedia article notes that the Egyptians had a special symbol for three fourths, so it may be an especially poor example regardless. A better example may be that of 7/10 = 1/2 + 1/5. --EncycloPetey 21:28, 17 September 2008 (UTC)

Thanks, your example is much better! Dbfirs 21:43, 17 September 2008 (UTC)

Not sure about what the Egyptians did, but in any case, they didn't speak English. The word is very much a modern word, used by mathematicians today, where it has the given senses (mainly the 1st).  :) Language Lover 03:22, 18 September 2008 (UTC)

I have no knowledge of Egyptian mathematics either, I was just guessing (and applying common sense). In any case, a simple example is better than a complicated one to illustrate modern mathematical usage. Dbfirs 05:47, 18 September 2008 (UTC)