96.33 A solution to the quartic equation

  title={96.33 A solution to the quartic equation},
  author={Michel Daoud Yacoub and Gustavo Fraidenraich},
  journal={The Mathematical Gazette},
  pages={271 - 275}
References 1. Ian Anderson, Sums of squares and binomial coefficients, Math. Gaz. 65 (June 1981) pp. 87-92. 2. D. R. Woodall, Finite sums, matrices, and induction, Math. Gaz. 65 (June 1981) pp. 92-103. 3. D. Desbrow, Sums of integer powers, Math. Gaz. 66 (June 1982) pp.97-100. 4. David Singmaster, Sums of squares and pyramidal numbers, Math. Gaz. 66 (June 1982) pp. 100-104. 5. D. Desbrow, Volumetric proof of the sum of squares formula, Math. Gaz. 83 (July 1999) pp. 256-257. TONY CRILLY 10… 

104.28 Extending Cardano‘s solution of the cubic

More generally, any matrix that preserves the quadratic form carries a point on the hyperboloid to another one. 3 × 3 x2 + y2 − z2 Although one can obtain parametrisations such as above, one cannot

Algorithm 954

An accurate and efficient algorithm for obtaining all roots of general real cubic and quartic polynomials and shows that a stable Newton-Raphson iteration on a derived symmetric sixth degree polynomial can be formulated for the real parts of the complex roots.

Algorithm 1010

The proposed algorithm is based on the decomposition of the quartic polynomial into two quadratics, whose coefficients are first accurately estimated by handling carefully numerical errors and afterward refined through the use of the Newton-Raphson method, which proves its absolute reliability as well as its efficiency.

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  • A. Rastegin
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Uncertainty relations in terms of min-entropies and Rényi entropies for POVMs assigned to a quantum design and relations of the Landau–Pollak type are addressed.



Sums of Integer Powers

In a recent article (this Gazette, 65 (1981), 87-92) Dr Anderson raised the question of the derivation of the well-known formula for the sum of integer squares, in contradistinction to its mere

Sums of Squares and Binomial Coefficients

before it has been derived. For example, (1) is needed when evaluating S0x dx from first principles, approximating to the area under the curve y = x by rectangles. It is then somewhat unsatisfactory

Sums of Squares and Pyramidal Numbers

In the June 1981 Gazette, Ian Anderson discussed several ways of finding the sum of the first n squares: His methods are mostly algebraic and I wondered if there were more geometric ways of obtaining

Finite Sums, Matrices and Induction

—which I suppose is useful if you happen to have access to an oracle that will generate these results for you. It is more useful if you can discover the results for yourself, and hardly any students

83.21 Volumetric proof of the sum of squares formula

Let m be a positive integer. Six rectangular boxes (one is illustrated in Figure 1), each with dimensions m x m x 1, and so with equal volumes m, can be assembled as Figure 3 illustrates, into a

Theory of equations

Solving quartics using palindromes, Math. Gaz

  • 1991

Solving quartics using palindromes

  • Math. Gaz