Talk:Cubic function

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Sorry about being a pain in the posterior.

Thanks JCSantos for fixing the brain farts that I had with my corrections. I really hate making such large changes as I did, particularly to a page that has an editor that knows what they are doing. But we have two different approaches to the article. My goal is to make the article as accessible as possible to high school students even. I don't want to speak to someone else's motivation but it seems that want to make it as technically correct and as engaging to a semi-expert as possible. In my mind these are both valid and complimentary approaches that can lead to lots of frustration if care is not taken. If taken too far both violate the spirit and the law of wikipedia.

In my last, admittedly very large and likely including a few errors, revision I attempted to make a compromise of sorts by factoring out a practical section. This too has its pitfalls and perhaps the only solution is to factor out some of it into a separate article. For example, in order to help more with accessibility I would eventually like to do an example using complex numbers. This is perilously close to violating the mission of wikipedia and if I did so I would feel probably feel obligated to split out a separate article due to issues with length and not overwhelming your good work.

The good news is that I am aware that I am making a mess. From now on my plan is to start cleaning up some of the mess that I made, instead of just making more.

I appreciate any patience that you can have with me. TStein (talk) 20:15, 7 June 2016 (UTC)

I like the way the article has come to look in the past few days. I had always thought that the article had so much content that it would be too intimidating to someone not already familiar with the topic. But the new organization is nice--just giving the various solutions first, then going into details. Thanks to both of you for all your work! Loraof (talk) 23:01, 7 June 2016 (UTC)

Numerical solution

I notice that my contribution—a fast numerical method for finding the real roots—was deleted twice. One of the reasons given was that the method is not widely used. Do you have statistics to prove that? Even if this were true: The method may become popular in the future. Solving cubic equations numerically is a major issue in chemical engineering, therefore this page should not be restricted to “exact” methods.

Thermo53 (talk) 12:28, 22 July 2016 (UTC)

Your contribution is original research, which has not been reliably published. As such, wikipedia is not a place for publishing it. See WP:No original research. D.Lazard (talk) 13:37, 22 July 2016 (UTC)

Hard-to-understand graphic

This animation shows the roots of x^3-3*x=cos(3*t) for different values of t; the roots are [2*cos(t), 2*cos(t+2*pi/3), 2*cos(t-2*pi/3)]

The section Cubic function#Trigonometric solution for three real roots had this graphic added to it on 12 October 2016. I just can't make heads or tails out of it. Can someone expand the caption to explain what the various colors (red, blue, green, black) are, how to interpret it, and so forth? Or, would there be any objection to my removing it? Loraof (talk) 21:18, 18 January 2017 (UTC)

I agree for removing the image. I cannot understand why it is a 3D plotting, when there is only 2 variables, t and the value of a root. The generating program appearing in the file is of no help, and seems to not correspond to the image (or to generate only a part of the image, as there is no plot instruction for a red curve nor for a blue curve). D.Lazard (talk) 21:53, 18 January 2017 (UTC)

Geometric interpretation of the roots

Is it possible that somebody puts into the section "Geometric interpretation of the roots" info about my new interpretation of the roots?
Please, see "Cubic polynomial roots" GeoGebra page and "Circumcircle of a polynomial" GeoGebra book
There is a paper in Russian
Yu. V. Vyazovetskii, A. S. Tikhonov, “Окружность, описанная вокруг многочлена”, Mat. Pros., Ser. 3, 15, MCCME, Moscow, 2011, 107–113 (in Russian)
(Ю. В. Вязовецкий, А. С. Тихонов, “Окружность, описанная вокруг многочлена”, Матем. просв., сер. 3, 15, Изд-во МЦНМО, М., 2011, 107–113)
see the paper or its dublicate.
I am afraid my English is imperfect to do this work. — Preceding unsigned comment added by Ast cubic (talk • contribs) 06:27, 19 August 2017 (UTC)

Apparently, this is your own research, which has not been reliably published (published in international peer reviewed journals), and is not referred to in any WP:secondary source. Therefore, this has not its place in Wikipedia, by the policy WP:NOR. D.Lazard (talk) 08:17, 19 August 2017 (UTC)

OK. I have no actual objections. I wish only to note that the paper is published in national (not international, but not deeply domestic) and peer reviewed (by E.B.Vinberg, the author of A Course in Algebra) journal and those journal volume (#15) contains an article written by Vladimir Arnold. I will look for another place to present paper's results since I am absolutely sure that the ideas and construction of the paper can be interesting to many lovers of mathematics. I would appreciate your advice. — Preceding unsigned comment added by Ast cubic (talk • contribs) 10:56, 19 August 2017 (UTC)

Another comment on a geometric interpretation of cubic function

Would it be possible to add some information on how the geometric solutions "worked"? That is, how they were constructed, interpreted, presented? For example, the article mentions Archimedes using the intersection of cones to approach the problem. What did that look like? Did he make physical, 3-dimensional cones, or did he use a 2-d representation of a cone (with perspective, perhaps?) What tools did he permit himself? I believe he made use of a "neusis construction" at some point, which allowed the solution of problems impossible with straight-edge and compass. How did this work? Why is a neusis more powerful? What algebraic tools does it add? How is this related to origami construction, which can also solve some cubic equations? There are so many interesting directions for this article to grow! Thanks greatly for reading. :) JonathanHopeThisIsUnique (talk) 19:51, 15 September 2017 (UTC)