Ancient Equation

People’s concerns mathematics dates back to ancient times. First steps to discerning life issues were counting, measuring, comparing, calculation of area or volume, solving problems and practical issues have led the man on the path of knowledge of practical necessities pleased to recognize ideas, to problematize. Thus crystallized math and scale development go from concrete to abstract.

It seems that the ancient Egyptians were concerned not only with the real problems of life, but also theoretical, invented seeking to generalize to find a mathematical model. Thus Ahmes’s manual “Rhind Papyrus” shows that Egyptians knew degree equations, fractions, calculate the approximate area of ​​the circle.

Practical issues (especially measurements) quite early led to equations of the second degree. Babylonian cuneiform writings math equations meet Tier II and even Tier II systems of equations with two unknowns.

Greek mathematics was concerned about the treatment of algebraic geometry problems. Hero of Alexandria (100 d. H.) took Babylonian and Egyptian tradition in the second degree equations using approximate square root formula. Square root has been a concern of Indian mathematicians, especially Bhaskar (144 d. H.). Methods have entered Europe through Arabic writings that contributed to their improvement.

Cubic equations were known to the ancient Greeks, Indians and Babylonians. Breakthroughs in the study of equations of third degree carried Hero of Alexandria succeeding numerical solving the cubic equation. The first step in kinda methods of calculation is due mathematicians Arabs and Indians. But all that knew how to solve equations of the second degree and third degree equation solver some have failed to discover formulas. The first who managed to do so seems to have been Scipione del Farro in Bologna, but his works were not published. Niccolo Tartaglia independent of it (1500-1557) found formulas for solving the laurels of success but have been taking Cardano.

Solving equations question of existence and finding solutions. The assumption that any equation of degree n n admits multitude of complex numbers roots was first raised by Dutchman Albert Girard (1595-1632). They tried to prove this assertion René Descartes (1596-1650), Jean d’Alembert (1717-1783) and others. The first demonstration of the fundamental theorem of algebra complex gave Gauss (1777-1855) in 1799. Later he also found various other demonstrations for this.

After the Renaissance found formulas for solving equations of grade III and IV, seventeenth and eighteenth centuries mathematicians have consistently focused on finding formulas for solving equations of degree V and higher. Gradually it came to recognize that solving algebraic equations of higher grade is not possible. Contributed to this Joseph- Louis Lagrange (1736-1813) and Carl- Friedrich Gauss (1777-1855).

In 1824, the Norwegian Niels Henrik Abel (1802-1829), a math genius manages to prove that the equation of the V (and therefore the higher grade) is not solvable by radicals after Paolo Ruffini in 1799 had a incomplete demonstration of this statement. Recognizing and acknowledging this was all the more difficult by the vast majority of special cases of algebraic equations of higher grade can be solved by radicals.

Later, the mathematician Evariste Galois (1811-1832) highlights the problem stating necessary and sufficient conditions as algebraic equation of greater or equal to five to be solved by radicals.