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The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics that include fractions, algebra, quadratic and cubic equations and the Pythagorean theorem. The Babylonian tablet YBC 7289 gives an approximation of 2 {\displaystyle {\sqrt {2}}} accurate to three significant sexagesimal digits (about six significant decimal digits).
Plimpton 322 is a Babylonian clay tablet, believed to have been written around 1800 BC, that contains a mathematical table written in cuneiform script.Each row of the table relates to a Pythagorean triple, that is, a triple of integers (,,) that satisfies the Pythagorean theorem, + =, the rule that equates the sum of the squares of the legs of a right triangle to the square of the hypotenuse.
Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.
This is a list of equations, by Wikipedia page under appropriate bands of their field. ... Polynomial equation. Linear equation; Quadratic equation; Cubic equation;
This crucial step completes a larger square of side length + . Completing the square is the oldest method of solving general quadratic equations, used in Old Babylonian clay tablets dating from 1800–1600 BCE
The oldest known record comes from Plimpton 322, a Babylonian clay tablet from about 1800 BC, written in a sexagesimal number system. [2] When searching for integer solutions, the equation a 2 + b 2 = c 2 is a Diophantine equation. Thus Pythagorean triples are among the oldest known solutions of a nonlinear Diophantine equation.
The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square. That formula always gives the roots of the quadratic equation, but the solutions are expressed in a form that often involves a quadratic irrational number, which is an algebraic fraction that can be evaluated ...
In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is + = (), =,,, … which gives rise to the sequence,,, … of iterated function applications , (), (()), … which is hoped to converge to a point .