His formula is again mentioned by Eutokios in a commentary on Archimedes. The Greek mathematician Hero of Alexandria devised a method for calculating cube roots in the 1st century CE. In the fourth century BCE Plato posed the problem of doubling the cube, which required a compass-and-straightedge construction of the edge of a cube with twice the volume of a given cube this required the construction, now known to be impossible, of the length 3√ 2.Ī method for extracting cube roots appears in The Nine Chapters on the Mathematical Art, a Chinese mathematical text compiled around the 2nd century BCE and commented on by Liu Hui in the 3rd century CE. The calculation of cube roots can be traced back to Babylonian mathematicians from as early as 1800 BCE. Quartic equations can also be solved in terms of cube roots and square roots. If two of the solutions are complex numbers, then all three solution expressions involve the real cube root of a real number, while if all three solutions are real numbers then they may be expressed in terms of the complex cube root of a complex number. The second equation combines each pair of fractions from the first into a single fraction, thus doubling the speed of convergence.Īppearance in solutions of third and fourth degree equations Ĭubic equations, which are polynomial equations of the third degree (meaning the highest power of the unknown is 3) can always be solved for their three solutions in terms of cube roots and square roots (although simpler expressions only in terms of square roots exist for all three solutions, if at least one of them is a rational number). For example, the real cube root of 8, denoted 8 3 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. In mathematics, a cube root of a number x is a number y such that y 3 = x. A unit cube (side = 1) and a cube with twice the volume (side = 3√ 2 = 1.2599.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
December 2022
Categories |