Noun:

மரக்கால் எட்டு காலன்,

quartic தமிழ் அர்த்தத்தின் உதாரணம்:

None

quartic's Usage Examples:

For the quartic (ab) 4 (aib2-a2b,) alb2 -4a7a2blb2+64a2 bib2 - 4a 1 a 2 b 7 b 2 + a a b i a,a 4 - 4ca,a 3 +6a2 - 4a3a3+ aoa4 2(a 0 a 4 - 4a1a3 +e3a2), one of the well-known invariants of the quartic.

4-2(f y 1) 2 connecting the Hessian with the quartic and its first and second polars; now a, a root of f, is also a root of Ox, and con se uentl the first polar 1 of of q y p f?This method of solution fails when the discriminant R vanishes, for then the Hessian has equal roots, as also the cubic f.

The simplest form to which the quartic is in general reducible is +6mxix2+x2, involving one parameter m; then Ox 2m (xi +x2) +2 (1-3m2) x2 ix2; i 2 (t +3m2); j '6m (1 - m) 2; t (1 - 9m 2) (xi - x2) (x21 + x2) x i x 2.

These curves are instances of unicursal bicircular quartics.

The forms of the non-singular quartics are very numerous, but it is not necessary to go further into the question.

Thus the ternary quartic is not, in general, expressible as a sum of five 4th powers as the counting of constants might have led one to expect, a theorem due to Sylvester.

The vanishing of the invariants i and j is the necessary and sufficient condition to ensure the quartic having three equal roots.

The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.

Xnyviaicos, ribbon), a quartic curve invented by Jacques Bernoulli (Acta Eruditorum, 1694) and afterwards investigated by Giulio Carlo Fagnano, who gave its principal properties and applied it to effect the division of a quadrant into 2 2 m, 3.

: these are the cubic itself of degree order I, 3; the Hessian of degree order 2, 2; the cubi-covariant G of degree order 3, 3, and the quartic invariant of degree order 4, o.

Lemniscate >>The name lemniscate is sometimes given to any crunodal quartic curve having only one real finite branch which is symmetric about the axis.

The quartic will have two pairs of equal roots, that is, will be a perfect square, if it and its Hessian merely differ by a numerical factor.

The same problems, or most of them, and also the elementary problems in regard to quartics are solved by Zeuthen, who in the elaborate memoir " Almindelige Egenskaber, 'c.

Synonyms:

biquadrate, number, biquadratic, fourth power,

Antonyms:

Arabic numeral, Roman numeral, minority, majority,