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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).
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
In stage 2, the well-attested Old Babylonian method of completing the square is used to solve what is effectively the system of equations b − a = 0.25, ab = 0.75. [6] Geometrically this is the problem of computing the lengths of the sides of a rectangle whose area A and side-length difference b − a are known, which was a recurring problem ...
An Old Babylonian tablet (Strasbourg 363) seeks the solution of a quadratic equation. [1] c. 1800 BC: The Plimpton 322 tablet gives a table of Pythagorean triples in Babylonian Cuneiform script. [2] 1800 BC: Berlin Papyrus 6619 (19th dynasty) contains a quadratic equation and its solution. [3] [4] 800 BC
Other topics covered by Babylonian mathematics include fractions, algebra, quadratic and cubic equations, and the calculation of regular numbers, and their reciprocal pairs. [29] The tablets also include multiplication tables and methods for solving linear, quadratic equations and cubic equations, a remarkable achievement for the time. [30]
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.
Al-jabr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. For example, x 2 = 40x − 4x 2 is reduced to 5x 2 = 40x. Al-muqābala is the process of bringing quantities of the same type to the same side of the equation. For example, x 2 + 14 = x + 5 is reduced to x 2 + 9 = x.
The tablets also include multiplication tables and methods for solving linear and quadratic equations. The Babylonian tablet YBC 7289 gives an approximation of √ 2 that is accurate to an equivalent of six decimal places. Babylonian mathematics were written using a sexagesimal (base-60) numeral system.