Search results
Results From The WOW.Com Content Network
The other roots of the equation are obtained either by changing of cube root or, equivalently, by multiplying the cube root by a primitive cube root of unity, that is . This formula for the roots is always correct except when p = q = 0 , with the proviso that if p = 0 , the square root is chosen so that C ≠ 0 .
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who stated it in 1643.
Descartes' rule of signs. In mathematics, Descartes' rule of signs, first described by René Descartes in his work La Géométrie, is a technique for getting information on the number of positive real roots of a polynomial. It asserts that the number of positive roots is at most the number of sign changes in the sequence of polynomial's ...
Doubling the cube, also known as the Delian problem, is an ancient [a] [1] : 9 geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to ...
Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k . A solution of a polynomial system is a set of values for the xi s which belong to some algebraically closed field extension K of k ...
René Descartes. René Descartes ( / deɪˈkɑːrt / day-KART or UK: / ˈdeɪkɑːrt / DAY-kart; French: [ʁəne dekaʁt] ⓘ; Latinized:Renatus Cartesius; [note 3] [11] 31 March 1596 – 11 February 1650) [12] [13] [14] : 58 was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern ...
La Géométrie. The work was the first to propose the idea of uniting algebra and geometry into a single subject [2] and invented an algebraic geometry called analytic geometry, which involves reducing geometry to a form of arithmetic and algebra and translating geometric shapes into algebraic equations. For its time this was ground-breaking.