Clebsch's equations, lines on a quartic surface having a nodal line, singular points of E.
But when the quartic is numerical the same thing happens as in the cubic, and the algebraical solution does not in every case give the numerical one.
For a quartic the formulae present themselves in a somewhat different form, by reason that 4 is not a prime number.
A non-singular quartic has only even circuits; it has at most four circuits external to each other, or two circuits one internal to the other, and in this last case the internal circuit has no double tangents or inflections.
We may further consider the inflections and double tangents, as well in general as in regard to cubic and quartic curves.
A quartic curve has 24 inflections; it was conjectured by George Salmon, and has been verified by H.
The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.
In many respects the Kummer quartic plays a part in three dimensions analogous to the general quartic curve in two; it further gives a natural representation of certain relations between hyperelliptic functions (cf.
The first class is equivalent to a quarticin four dimensions and is always rational, but the latter class has to be subdivided into the elliptic and the rational, just like twisted quartic curves.
The focal surface is of degree four and class 2m; this kind of quartic surface has been extensively studied by Kummer, Cayley, Rohn and others.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "quartic" in a variety of sentences. We hope that you will now be able to make sentences using this word. Other words: foursquare; quadrilateral; quadruped; quaternary
