Talk:Spiric section

Spiric curves
I know "spiric sections" by the name "spiric curves". see.: www-history.mcs.st-and.ac.uk/mathematicians/perseus.html
 * I think in that article, "spiric curve" follows from "spiric" which is short for "spiric section". I added the the link, seems to be an old version of a MacTutor link, to the article.--RDBury (talk) 13:33, 21 September 2009 (UTC)

Variations in the definition
The French site, Encyclopédie des Formes Mathématiques Remarquables (see refs section), uses an algebraic definition of the curve rather than a geometric one. This would not be a problem if the definitions were equivalent, but in this case they are not. Specifically, the algebraic definition includes the curves obtained as the intersection of the torus with the plane z=ic as well as z=c. In other words the algebraic definition allows sections by imaginary planes as well as real ones. The curves produced do exist, even when restricted to x and y real, and are different than the ones produced in the geometrical definition, for example some parameters give a pair of crescent shapes. I haven't found enough sources on this subject to determine if the algebraic definition is the modern standard or just an extension created by the author of that site. I personally like the algebraic definition better, families of curves similar to this can often be defined in several, surprisingly diverse ways and using the more inclusive definition will probably eliminate exceptional cases.--RDBury (talk) 14:10, 21 September 2009 (UTC)

Polar coordinates
Are there any reasons to complicate the last formula? It 's easier this way
 * $$r^4=r^2(d\cos^2\theta+e\sin^2\theta)+f. $$

Also, this formula leads to a simple explicit formula for constructing a curve.
 * $$ \theta=F(r^2)$$

Not interested? Сурбас (talk) 09:37, 28 September 2022 (UTC)