An algebraic equation of the fourth power; quartic equation.
(mathematics) Of a polynomial expression, involving only the second and fourth powers of a variable, as x4 + 3x2 + 2. Sometimes extended to any expression involving the biquadrate or fourth power (but no higher powers), as x4 − 4x3 + 3x2 − x + 1.
In the geometry of plane curves, the term parabola is often used to denote the curves given by the general equation a' n x n = ym+n, thus ax= y 2 is the quadratic or Apollonian parabola; a 2 x = y 3 is the cubic parabola, a 3 x = y4 is the biquadratic parabola; semi parabolas have the general equation ax n-1 = yn, thus ax e = y 3 is the semicubical parabola and ax 3 = y 4 the semibiquadratic parabola.
Running through these volumes in order, we have in the second the memoir, Summatio quarundam serierum singularium, the memoirs on the theory of biquadratic residues, in which the notion of complex numbers of the form a--bi was first introduced into the theory of numbers; and included in the Nachlass are some valuable tables.
He was professor of mathematics in the university of Deseret and wrote several books on this subject, these including Cubic and Biquadratic Equations (1866).
This concept is extended to algebra: since a line, surface and solid are represented by linear, quadratic and cubic equations, and are of one, two and three dimensions; a biquadratic equation has its highest terms of four dimensions, and, in general, an equation in any number of variables which has the greatest sum of the indices of any term equal to n is said to have n dimensions.