Talk:Pronic number/Archive 1

Sloane's OEIS says that pronic number is the right term and heteromecic number is a misnomer. However, at MathWorld, "pronic number" is a redirect to "heteromecic number". The term oblong number I have only seen at MathWorld, listed as yet another possible term for this same concept. So I decided to take my cue from MathWorld, and thus I made "pronic" and "oblong" as redirects to "heteromecic". PrimeFan 21:39, 14 May 2004 (UTC)


 * For what it's worth, I've seen "pronic" at least a few times in the literature, and "oblong" seems vaguely familiar, but I've never heard of "heteromecic". 4pq1injbok 21:30, 16 Jul 2004 (UTC)  Update: currently, at MathWorld, "heteromecic number" redirects to "pronic number".  So I propose to make "pronic number"  our main article.  4pq1injbok 22:04, 16 Jul 2004 (UTC)


 * I've never seen either of the three terms in a book, I've only seen them online. If you go ahead and move this article to pronic number then I volunteer to gradually change the links into direct links. PrimeFan 20:30, 19 Jul 2004 (UTC)


 * I'll move it. Is there a special way to move pages other than copying and pasting the text? 4pq1injbok 03:01, 25 Jul 2004 (UTC)


 * Yes, there is. At the top of the page, just below "userName My talk Preferences My watchlist..." there are the tabs "Article Discussion Edit this page History Move (Un)Watch". Click the "Move" tab. Be sure to read all the instructions and notes, and to give some thought to whether or not the Talk page needs to be moved also. PrimeFan 20:44, 25 Jul 2004 (UTC)


 * Thanks, that shoulda been obvious. 4pq1injbok 13:05, 26 Jul 2004 (UTC)

Regarding Anton Mravcek's change on 2 June, re squarefreedom and squarefilth, it is true that
 * If neither n nor its following neighbor are squarefree, then obviously neither will be the resulting heteromecic number.

but it remains when we substitute either nonsquarefree or squareful for squarefree. This is since two consecutive integers cannot share a prime factor. 4pq1injbok 21:43, 16 Jul 2004 (UTC) Ah, I see that I missed the either -> neither in that revision, so this is not so relevant. Do note, however, that squareful is not an antonym for squarefree. 4pq1injbok 22:20, 16 Jul 2004 (UTC)


 * I used to think that, and it's undertandable. I'm going to read those two articles to see if they make the distinction clear. PrimeFan 20:30, 19 Jul 2004 (UTC)

indexing of heteromecic numbers
In looking at what links here, I noticed that Decagonal and Duodecagonal implied the nth heteromecic number was n^2 - n, however this page and Octoganal used n^2 + n. I edited the first two to match, someone fix it all if that does not make it correct. --Walt 12:19, 22 June 2006 (UTC)

etymology
What's the source of the word pronic? —Tamfang (talk) 04:55, 15 February 2008 (UTC)
 * According to a mispelling of promekes the Greek for oblong, going back at least as far as Euler. According to  προμήκης can mean prolonged, elongated, protruding, oblong, of numbers made up of two unequal factors. --Rumping (talk) 01:12, 30 March 2009 (UTC)

"Heteromecic" appears in F. Cajori's A History of Elementary Mathematics and he credits the term to the Pythagoreans. (pg 29)

also have in my notes that : Pronic seems to be a misspelling of promic, from the Greek promekes, for rectangular, oblate or oblong. Neither pronic nor promic seems to appear in most modern dictionaries. Richard Guy pointed out to the Hyacinthos newsgroup that pronic had been used by Euler in series one, volume fifteen of his Opera, so the mathematical use of the "n" form has a long history. — Preceding comment added by E.E. "Pat" Ballew

Just one more note as to the antiquity of heteromecic, In his translation of Euclid's "Elements", Sir Thomas Heath translates the Greek word 'eteromhkes[hetero mekes - literally "different lengths"] in Book one, Definition 22 as oblong. 88.108.117.184 (talk) 18:42, 26 September 2011 (UTC)
 * Pronic appears in 15th century Italian mathematical texts and had probably already shifted to the "n" spelling before it entered English.  Spinning Spark  19:43, 26 September 2011 (UTC)