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In the early 16th century, the Italian mathematician Scipione del Ferro (1465–1526) found a method for solving a class of cubic equations, namely those of the form x 3 + mx = n. In fact, all cubic equations can be reduced to this form if one allows m and n to be negative, but negative numbers were not known to him at that time. Del Ferro kept ...
The graph of any cubic function is similar to such a curve. The graph of a cubic function is a cubic curve, though many cubic curves are not graphs of functions. Although cubic functions depend on four parameters, their graph can have only very few shapes. In fact, the graph of a cubic function is always similar to the graph of a function of ...
This is a cubic equation in y. Solve for y using any method for solving such equations (e.g. conversion to a reduced cubic and application of Cardano's formula). Any of the three possible roots will do.
The book, which is divided into forty chapters, contains the first published algebraic solution to cubic and quartic equations.Cardano acknowledges that Tartaglia gave him the formula for solving a type of cubic equations and that the same formula had been discovered by Scipione del Ferro.
There are conjectures about whether del Ferro worked on a solution to the cubic equation as a result of Luca Pacioli's short tenure at the University of Bologna in 1501–1502. Pacioli had previously declared in Summa de arithmetica that he believed a solution to the equation to be impossible, fueling wide interest in the mathematical community.
In 1936, Margherita Piazzola Beloch showed how Lill's method could be adapted to solve cubic equations using paper folding. [6] If simultaneous folds are allowed, then any n th-degree equation with a real root can be solved using n − 2 simultaneous folds. [7]
The cubic-plus-chain (CPC) [28] [29] [30] equation of state hybridizes the classical cubic equation of state with the SAFT chain term. [21] [22] The addition of the chain term allows the model to be capable of capturing the physics of both short-chain and long-chain non-associating components ranging from alkanes to polymers. The CPC monomer ...
[12] [13] Cubic equations were known to the ancient Greek mathematician Diophantus. [14] Hero of Alexandria devised a method for calculating cube roots in the 1st century CE. [ 15 ] Methods for solving cubic equations and extracting cube roots appear in The Nine Chapters on the Mathematical Art , a Chinese mathematical text compiled around the ...