Talk:Doubling the cube

Links
What about links to the other two unsolvable problems? --Paughsw 05:00, 22 September 2005 (UTC)

I have a very very close solution, accurate within 0.000103 of an inch. Directions to the "almost" proof are here: http://www.cut-the-knot.org/cgi-bin/dcforum/ctk.cgi?az=read_count&om=703&forum=DCForumID4&omm=3&viewmode=threaded

Larouche link?
Do we want to keep it? While it is a moderately nice little script, it functions as part of the general promotion of Larouche's bizaare claims that the problem is somehow solvable. This is not a good. JoshuaZ 03:23, 25 January 2007 (UTC)

Legend?
For a legend, the Delian story included remarkably precise dates, and lies well within the historical era. It would perhaps be useful to mention the source of the legend, that is to say where it was first recorded as a story. -- Cimon Avaro; on a pogostick. (talk) 05:48, 18 March 2009 (UTC)


 * I rewrote the section and removed the word legend, though really the story could well be called a legend in the "urban legend" sense of the word. The sources I've found give conflicting versions of the tale and speak of forged letters and different people quoting originals that are now lost, but most of them agree that the story is at best implausible. There could be a lot more done in tracing down the history of the story but given that main purpose in including is to explain the name of the problem it's probably best not to go overboard on detail.--RDBury (talk) 05:24, 31 October 2009 (UTC)

Archytas Solution?
According to "Encyclopedia of Classical Philosophy" edited by Donald J. Zeyl. Archytas: "Geometry and mechanics were brought together in his method of finding the two mean proportionals necessary in order to solve the famous problem of duplicating the cube (Eutocius in Archim. Sphaer. et Cyl. 2)." — Preceding unsigned comment added by Thistleknot (talk • contribs) 04:18, 16 February 2015 (UTC)

Error in solution
Please recheck consrtuction of AG. I got that AG is 2/sqrt(3). — Preceding unsigned comment added by 95.68.125.105 (talk) 10:28, 14 June 2012 (UTC)


 * I just checked it myself and came out with the cube root of 2 plus it has a citation which gives a proof. I'm not sure how anyone ever thought of the construction though! Dmcq (talk) 12:51, 14 June 2012 (UTC)

I concur. Not even checking the result, the argument has obvious faults. Can somebody please reformulate it so it starts making sense?

Vlad Patryshev (talk) 16:13, 23 December 2013 (UTC)
 * It isn't an argument. It is a description. I believe the result is correct. What makes you think it is wrong? Dmcq (talk) 20:03, 23 December 2013 (UTC)
 * In fact if you look up the citation you'll see a proof. Dmcq (talk) 20:42, 23 December 2013 (UTC)

Constructability
construct a series of volumes 2,4,8,16 cu in round the cube roots to 2 decimal points and cube. The results are good to machine made tolerances. 2 cube root = 1.2599210498948731647672106072782, ^3 = 2 1.26 ^3 = 2.000376 in board measure the side of a 5/4 board as the side of your cube of volume 2 cubic in 4 cube root 1.5874010519681994747517056392723, ^3 = 4 1.59 ^3 = 4.019679 in board measure the side of a 6/4 board as the side of your cube of volume 4 cubic in 8 cube root =2, ^3 = 8 in board measure the side of a 8/4 board as the side of your cube of volume 8 cubic in 2.5198420997897463295344212145565, ^3 =16 16 cube root 2.52, ^3 = 16.003008 in board measure the side of a 10/4 board as the side of your cube of volume 16 cubic in 142.0.102.183 (talk) 20:09, 5 January 2016 (UTC)

Doubling the cube is now known to be impossible using only a compass and straightedge: Still true?
This is the first time I have contributed anything to Wikipedia besides donations, so I'm not sure what exactly I'm doing here. And I am not a mathematician for sure, but I wanted to at least point out something in this article that may no longer reflect current knowledge.

The latest Scientific American Magazine (October 2021 Volume 325, Issue 4 ) features an article on math entitled "Infinity Category Theory Offers a Bird's-Eye View of Mathematics" by Emily Riehl which seems to indicate that it is now possible to construct "with an imaginary straightedge and compass, a cube with a volume twice that of a different, given cube".

Just trying to make Wikipedia better in my own diminutive way. I'll check back to see which part of subterranean hell this post has been banished to bc that's how I learn. Thanks. Glenn Wiens GAWiens (talk) 03:57, 21 October 2021 (UTC)
 * That is not even close to an accurate description of the article you link. Yes, the proof that it's impossible is still valid. As the article says. —David Eppstein (talk) 05:10, 21 October 2021 (UTC)
 * Yes - I see that now. My bad. I'll stick to conventional contributions in the future. GAWiens (talk) 00:42, 22 October 2021 (UTC)

Intro
- ''«Also revert disimprovement to final sentence of lead paragraph. "The solution was known to work with other tools": There are many solutions, different ones of which work with different tools.»''
 * Solutions* were given literally few words earlier in the prior sentence. The original sentence is spelled wrongly I'm afraid.

AXO NOV (talk) ⚑ 10:45, 29 January 2022 (UTC)
 * This thread has no apparent purpose. What exactly do you want? 82.132.213.165 (talk) 14:50, 29 January 2022 (UTC)

Segment lengths
- «Re lengths of what?: that were given literally two words earlier in the same sentence»
 * Segments probably meant to be edges of the cube, which for the purposes of proof were named as segments. It's just a bit confusing. Needs clarification. Best.

AXO NOV (talk) ⚑ 10:45, 29 January 2022 (UTC)
 * Nothing was remotely unclear or confusing in that sentence. 82.132.213.165 (talk) 14:51, 29 January 2022 (UTC)
 * The phrase in question was "Given segments of lengths a and 2a, ...". This means: suppose someone gives us segments, and the lengths of the segments that they give us are the numbers a and 2a. It is not ambiguous. —David Eppstein (talk) 17:34, 29 January 2022 (UTC)

Wrong math construct?
In the section "In music theory" the last sentence starts "It multiplies the frequency of a tone by". Then follow constructions which appear to be representing the fractions "two and four-twelfths" and "two and one-third", but these numbers should actually be "two to the power of 4 over 12" and "two to the power of one-third". Someone please fix it - I have no idea how to (or even if it IS supposed to be representing powers but only looks wrong). 194.193.181.245 (talk) 15:43, 9 March 2022 (UTC)
 * Fixed. Thanks for catching this. —David Eppstein (talk) 16:17, 9 March 2022 (UTC)


 * @David Eppstein Thanks for fixing it (it seems to have been a group effort), but what was my conflict of interest?  Former 194.193.181.245 194.193.149.112 (talk) 08:35, 14 March 2022 (UTC)


 * @194.193.181.245  If this bulk underlining is incorrect, I apologise. I didn't know why it happened or how to stop it (but now I think my error was inserting text to try and keep the IP address for the "Former"). 194.193.149.112 (talk) 08:41, 14 March 2022 (UTC)

Clarity in the instructions
In constructing the first exercise, you need to mark the required length on the *ruler*, not the page. Then, the last instruction, you are supposed to rotate the ruler taking A as the axis until you get a line segment between BE and DF, which is of the required length. Only then is AG the required length. 49.206.14.116 (talk) 12:51, 26 June 2022 (UTC)