Talk:Neusis construction

This article is a translation from my contribution to the Dutch wikipedia. I may have translated wrongly two technical terms, viz.: I will be grateful for any corrections! Hans van Deukeren
 * guiding line (?) = directrix (?). In German this is called "Leitlinie";
 * catch line (?). The German equivalent is "Fanglinie".

There are difficulties with this article
 * It implies that Archimedes, when neusis was popular, was before Plato, when its popularity waned.
 * It ignores the difference between pure and applied mathemetics.
 * It therefore omits the clear reason Euclid confined himself to compass and straightedge: they are the only tools whose behavior was described in his axioms, and therefore the only ones about which he could prove anything. Septentrionalis 00:02, 1 April 2006 (UTC)

Question about the algebraic power of the neusis construction
Hello! Does anyone know the algebraic power of neusis construction? As in, what is the equivalent of "constructible numbers" for neusis construction? Is neusis construction strictly "stronger" than compass and straightedge? Since it can solve some problems impossible with only compass and straightedge? Or are there any problems not solvable with neusis, that are solvable with compass and straightedge? — Preceding unsigned comment added by JonathanHopeThisIsUnique (talk • contribs) 19:36, 20 June 2018 (UTC)
 * I can't give you a direct answer, but you likely wish to compare this to the Mathematics of paper folding & the Huzita–Hatori axioms, especially axiom number 6. --No identd (talk) 23:31, 24 June 2018 (UTC)
 * Oh! Thanks for your reply! I'll look into that. :) JonathanHopeThisIsUnique (talk) 17:25, 29 June 2018 (UTC)
 * I got some interesting information that may be of use, although it's somewhat high level for me. I'll put the links here so I don't forget. They might also be useful for anyone else who is interested in improving the article.


 * http://math.ucr.edu/~res/math153/history09c.pdf
 * https://mathoverflow.net/questions/31944/neusis-constructions
 * JonathanHopeThisIsUnique (talk) 17:46, 29 June 2018 (UTC)
 * The main thing I understood is that there are different "types" of neusis construction (line-line, line-circle, circle-circle) and that these different types of construction have different power. Line-circle is known to be stronger than line-line. It is unknown if circle-circle is more powerful than line-circle, though it is known to be at least as powerful. JonathanHopeThisIsUnique (talk) 17:50, 29 June 2018 (UTC)

Lines?
Is it correct to call l and m "lines"? I think that to a mathematician "line" means infinitely extending straight line. Aren't l and m more properly called curves? 86.132.223.101 (talk) 17:55, 30 March 2017 (UTC)

Overlapping Properties with a Compass and Straight Edge
The pole can simply be considered a pivot as with the usual compass. The explanation of the neusis is vague, but it appears that you want an adjustable length, yet movable line segment with a bull's eye centered on the directrix. You would put a writing utensil on the center bull's eye to produce desired geometric construction. For the life of me I cannot find an actual physical neusis. We may have to build our own.

Important to note, absolutely anything you can rotate where you can fix one point in space, and place a writing utensil at the fixed radius can serve as a compass for all intents and purposes. Draftsmen likely recall there are superior compass designs that don't require gouging the writing surface at all as with the traditional compass. — Preceding unsigned comment added by Jakewayd (talk • contribs) 00:41, 10 September 2018 (UTC)

Failure?
I fail to see how the angle is trisected in the diagram. To me, points A and B seem completely random… CielProfond (talk) 21:37, 27 December 2023 (UTC)


 * AB is the same length as the radius (OP)—If B is placed on the arc and A on the baseline in such a way that AB passes through the point P, there is only one position where the “ruler” AB can fulfill that condition.
 * —Just what this —“ For angles θ < 135° the same construction applies, but with P extended beyond AB.”— means is completely unclear to me though 2001:5B0:2711:4318:404C:E27:FD20:EF3 (talk) 07:02, 10 February 2024 (UTC)


 * Oh! I get it! However, it should be more clearly explained on the article page. As for the θ < 135° thing, my tries show that P then lies on a vertical line starting at O. This, too, should be clearly explained on the article page.