# Talk:Cubic plane curve

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The recent edit replacing Weierstrass form by elliptic functions actually is over-specific (assumes base field is the complex numbers); it misses out cases of importance, e.g. over a finite field in cryptology. Charles Matthews 16:48, 22 Jul 2004 (UTC)

Not sure about the inflection points being 9, over a field of characteristic 3. Charles Matthews 20:41, 12 April 2006 (UTC)

"It is easily proved that a plane curve of the third degree (or cubic) possesses nine points of inflexion, ...", "Space and Time" by Emile Borel, p. 90 --JKSellers (talk) 08:09, 15 January 2008 (UTC)

## Cuspidal cubic

Cuspidal cubic redirects here but the word "cuspidal" is never mentioned. 130.236.62.69 (talk) 11:28, 21 May 2012 (UTC)

## Locus of a point

Why does the article repeatedly use the term "locus of a point X [satisfying a condition]"? Should it be the locus of points such that for a point X a condition holds, or is there a usage history of this form? ᛭ LokiClock (talk) 11:03, 22 September 2013 (UTC)

I have added a wikilink for "locus". Nevertheless there remain two qiestions
• The article uses "locus of a point ..." where I would write "locus of the points ...", because there are many points in a locus. I am not sure of the correct formulation.
• Locus (mathematics) defines "locus" as a synonymous of "set of points such that ...". Here it is used for "closure of the set of the points such that ..." or, equivalently, "set of points such that, generically, ...". In fact, there may be some points on the cubic that do not satisfy the condition, when the method of construction degenerates. I believe that, in modern mathematics, this is the second meaning that is commonly used, but some verification is needed.
In any case, the whole section "Cubic curves in the plane of a triangle" deserve a complete rewriting as being too technical and insufficiently wikilinked and sourced. D.Lazard (talk) 13:09, 22 September 2013 (UTC)

## History

There should be a section entitled "History" here. The cissoid of Diocles seems to have been a cubic curve. — Preceding unsigned comment added by 79.77.128.149 (talk) 10:38, 23 September 2016 (UTC)